There was, famously, a judge in Florida that said cryptocurrency was not money because you couldn't put it underneath your bed, and that's what money is: something that is tangible. So different people are going to have different decisions. And that's not just true for crypto, but also other areas of the law.

Your best-known crypto decisions strongly assert that crypto is traceable. One way people try to make it less traceable is with mixers, and Tornado Cash was sanctioned by OFAC not too long ago. Do you think the legal reasoning was sound enough for similar sanctions to be applied to other mixers, or decentralized exchanges?

I don't know. I think there's been some discussion that people may litigate some of these things, so I can't comment, because those frequently do come to our courthouse. And I think there are certainly people opining on that, yes and no.

So much of what judges do is that we rely on the parties that are before us to tell us what's right and what's wrong. And then, you know, obviously, they'll have different views, and we make a decision based on what people say in front of us. Are you aware that some legal analysis of the Tornado Cash sanctions references your recent decision in a cryptocurrency sanctions case?

That's what good lawyers will always do. Even legislators might look at that as they try to think about where the gaps are. As a prosecutor I had a case where we sued three Chinese banks to give us their bank records, and it had never been done before. Afterwards, Congress passed a new law, using the decisions from judges in this court and the D.

circuit court, the court above us. So I'm sure people look at prior decisions and try to apply them in the ways that they want to. Are there any misconceptions about how the law applies to crypto, or how your decisions should be interpreted, that you wish you could get across? One misconception is that the judges can't understand this technology — we can. People have these views in two extremes. The lawyer's fundamental job is to take super complex and technical things and boil them down to very easily digestible arguments for a judge, for a jury, or whoever it might be.

The financial technology transformation is driving competition, creating consumer choice, and shaping the future of finance. Hear from seven fintech leaders who are reshaping the future of finance, and join the inaugural Financial Technology Association Fintech Summit to learn more.

Financial technology is breaking down barriers to financial services and delivering value to consumers, small businesses, and the economy.

Fintech puts American consumers at the center of their finances and helps them manage their money responsibly. From payment apps to budgeting and investing tools and alternative credit options, fintech makes it easier for consumers to pay for their purchases and build better financial habits.

Fintech also arms small businesses with the financial tools for success, including low-cost banking services, digital accounting services, and expanded access to capital.

We advocate for modernized financial policies and regulations that allow fintech innovation to drive competition in the economy and expand consumer choice. Spots are still available for this hybrid event, and you can RSVP here to save your seat. Join us as we discuss how to shape the future of finance. In its broadest sense, Open Banking has created a secure and connected ecosystem that has led to an explosion of new and innovative solutions that benefit the customer, rapidly revolutionizing not just the banking industry but the way all companies do business.

Target benefits are delivered through speed, transparency, and security, and their impact can be seen across a diverse range of use cases. Sharing financial data across providers can enable a customer individual or business to have real-time access to multiple bank accounts across multiple institutions all in one platform, saving time and helping consumers get a more accurate picture of their own finances before taking on debt, providing a more reliable indication than most lending guidelines currently do.

Companies can also create carefully refined marketing profiles and therefore, finely tune their services to the specific need. Open Banking platforms like Klarna Kosma also provide a unique opportunity for businesses to overlay additional tools that add real value for users and deepen their customer relationships. The increased transparency brought about by Open Banking brings a vast array of additional benefits, such as helping fraud detection companies better monitor customer accounts and identify problems much earlier.

The list of new value-add solutions continues to grow. The speed of business has never been faster than it is today. For small business owners, time is at a premium as they are wearing multiple hats every day. Macroeconomic challenges like inflation and supply chain issues are making successful money and cash flow management even more challenging. This presents a tremendous opportunity that innovation in fintech can solve by speeding up money movement, increasing access to capital, and making it easier to manage business operations in a central place.

Fintech offers innovative products and services where outdated practices and processes offer limited options. For example, fintech is enabling increased access to capital for business owners from diverse and varying backgrounds by leveraging alternative data to evaluate creditworthiness and risk models.

This can positively impact all types of business owners, but especially those underserved by traditional financial service models. When we look across the Intuit QuickBooks platform and the overall fintech ecosystem, we see a variety of innovations fueled by AI and data science that are helping small businesses succeed. By efficiently embedding and connecting financial services like banking, payments, and lending to help small businesses, we can reinvent how SMBs get paid and enable greater access to the vital funds they need at critical points in their journey.

Overall, we see fintech as empowering people who have been left behind by antiquated financial systems, giving them real-time insights, tips, and tools they need to turn their financial dreams into a reality. Innovations in payments and financial technologies have helped transform daily life for millions of people. People who are unbanked often rely on more expensive alternative financial products AFPs such as payday loans, money orders, and other expensive credit facilities that typically charge higher fees and interest rates, making it more likely that people have to dip into their savings to stay afloat.

A few examples include:. Mobile wallets - The unbanked may not have traditional bank accounts but can have verified mobile wallet accounts for shopping and bill payments. Their mobile wallet identity can be used to open a virtual bank account for secure and convenient online banking. Minimal to no-fee banking services - Fintech companies typically have much lower acquisition and operating costs than traditional financial institutions.

They are then able to pass on these savings in the form of no-fee or no-minimum-balance products to their customers. This enables immigrants and other populations that may be underbanked to move up the credit lifecycle to get additional forms of credit such as auto, home and education loans, etc. Entrepreneurs from every background, in every part of the world, should be empowered to start and scale global businesses.

Most businesses still face daunting challenges with very basic matters. These are still very manually intensive processes, and they are barriers to entrepreneurship in the form of paperwork, PDFs, faxes, and forms.

Stripe is working to solve these rather mundane and boring challenges, almost always with an application programming interface that simplifies complex processes into a few clicks. Stripe powers nearly half a million businesses in rural America. The internet economy is just beginning to make a real difference for businesses of all sizes in all kinds of places. We are excited about this future. The way we make decisions on credit should be fair and inclusive and done in a way that takes into account a greater picture of a person.

Lenders can better serve their borrowers with more data and better math. Zest AI has successfully built a compliant, consistent, and equitable AI-automated underwriting technology that lenders can utilize to help make their credit decisions. While artificial intelligence AI systems have been a tool historically used by sophisticated investors to maximize their returns, newer and more advanced AI systems will be the key innovation to democratize access to financial systems in the future.

D espite privacy, ethics, and bias issues that remain to be resolved with AI systems, the good news is that as large r datasets become progressively easier to interconnect, AI and related natural language processing NLP technology innovations are increasingly able to equalize access.

T he even better news is that this democratization is taking multiple forms. AI can be used to provide risk assessments necessary to bank those under-served or denied access. AI systems can also retrieve troves of data not used in traditional credit reports, including personal cash flow, payment applications usage, on-time utility payments, and other data buried within large datasets, to create fair and more accurate risk assessments essential to obtain credit and other financial services.

By expanding credit availability to historically underserved communities, AI enables them to gain credit and build wealth. Additionally, personalized portfolio management will become available to more people with the implementation and advancement of AI. Sophisticated financial advice and routine oversight, typically reserved for traditional investors, will allow individuals, including marginalized and low-income people, to maximize the value of their financial portfolios.

Moreover, when coupled with NLP technologies, even greater democratization can result as inexperienced investors can interact with AI systems in plain English, while providing an easier interface to financial markets than existing execution tools. Open finance technology enables millions of people to use the apps and services that they rely on to manage their financial lives — from overdraft protection, to money management, investing for retirement, or building credit. More than 8 in 10 Americans are now using digital finance tools powered by open finance.

This is because consumers see something they like or want — a new choice, more options, or lower costs. What is open finance? At its core, it is about putting consumers in control of their own data and allowing them to use it to get a better deal. When people can easily switch to another company and bring their financial history with them, that presents real competition to legacy services and forces everyone to improve, with positive results for consumers.

For example, we see the impact this is having on large players being forced to drop overdraft fees or to compete to deliver products consumers want. We see the benefits of open finance first hand at Plaid, as we support thousands of companies, from the biggest fintechs, to startups, to large and small banks.

All are building products that depend on one thing - consumers' ability to securely share their data to use different services.

Open finance has supported more inclusive, competitive financial systems for consumers and small businesses in the U. and across the globe — and there is room to do much more. As an example, the National Consumer Law Consumer recently put out a new report that looked at consumers providing access to their bank account data so their rent payments could inform their mortgage underwriting and help build credit.

This is part of the promise of open finance. At Plaid, we believe a consumer should have a right to their own data, and agency over that data, no matter where it sits. This will be essential to securing benefits of open finance for consumers for many years to come. As AWS preps for its annual re:Invent conference, Adam Selipsky talks product strategy, support for hybrid environments, and the value of the cloud in uncertain economic times.

Donna Goodison dgoodison is Protocol's senior reporter focusing on enterprise infrastructure technology, from the 'Big 3' cloud computing providers to data centers.

She previously covered the public cloud at CRN after 15 years as a business reporter for the Boston Herald. AWS is gearing up for re:Invent, its annual cloud computing conference where announcements this year are expected to focus on its end-to-end data strategy and delivering new industry-specific services.

Both prongs of that are important. But cost-cutting is a reality for many customers given the worldwide economic turmoil, and AWS has seen an increase in customers looking to control their cloud spending. By the way, they should be doing that all the time. The motivation's just a little bit higher in the current economic situation. This interview has been edited and condensed for clarity.

Besides the sheer growth of AWS, what do you think has changed the most while you were at Tableau? Were you surprised by anything? The number of customers who are now deeply deployed on AWS, deployed in the cloud, in a way that's fundamental to their business and fundamental to their success surprised me. There was a time years ago where there were not that many enterprise CEOs who were well-versed in the cloud.

It's not just about deploying technology. The conversation that I most end up having with CEOs is about organizational transformation. It is about how they can put data at the center of their decision-making in a way that most organizations have never actually done in their history.

And it's about using the cloud to innovate more quickly and to drive speed into their organizations. Those are cultural characteristics, not technology characteristics, and those have organizational implications about how they organize and what teams they need to have. It turns out that while the technology is sophisticated, deploying the technology is arguably the lesser challenge compared with how do you mold and shape the organization to best take advantage of all the benefits that the cloud is providing.

How has your experience at Tableau affected AWS and how you think about putting your stamp on AWS? I, personally, have just spent almost five years deeply immersed in the world of data and analytics and business intelligence, and hopefully I learned something during that time about those topics. I'm able to bring back a real insider's view, if you will, about where that world is heading — data, analytics, databases, machine learning, and how all those things come together, and how you really need to view what's happening with data as an end-to-end story.

It's not about having a point solution for a database or an analytic service, it's really about understanding the flow of data from when it comes into your organization all the way through the other end, where people are collaborating and sharing and making decisions based on that data.

AWS has tremendous resources devoted in all these areas. Can you talk about the intersection of data and machine learning and how you see that playing out in the next couple of years?

What we're seeing is three areas really coming together: You've got databases, analytics capabilities, and machine learning, and it's sort of like a Venn diagram with a partial overlap of those three circles.

There are areas of each which are arguably still independent from each other, but there's a very large and a very powerful intersection of the three — to the point where we've actually organized inside of AWS around that and have a single leader for all of those areas to really help bring those together.

There's so much data in the world, and the amount of it continues to explode. We were saying that five years ago, and it's even more true today. The rate of growth is only accelerating. It's a huge opportunity and a huge problem. A lot of people are drowning in their data and don't know how to use it to make decisions. Other organizations have figured out how to use these very powerful technologies to really gain insights rapidly from their data.

What we're really trying to do is to look at that end-to-end journey of data and to build really compelling, powerful capabilities and services at each stop in that data journey and then…knit all that together with strong concepts like governance. By putting good governance in place about who has access to what data and where you want to be careful within those guardrails that you set up, you can then set people free to be creative and to explore all the data that's available to them.

AWS has more than services now. Have you hit the peak for that or can you sustain that growth? We're not done building yet, and I don't know when we ever will be. We continue to both release new services because customers need them and they ask us for them and, at the same time, we've put tremendous effort into adding new capabilities inside of the existing services that we've already built. We don't just build a service and move on.

Inside of each of our services — you can pick any example — we're just adding new capabilities all the time. One of our focuses now is to make sure that we're really helping customers to connect and integrate between our different services. So those kinds of capabilities — both building new services, deepening our feature set within existing services, and integrating across our services — are all really important areas that we'll continue to invest in.

Do customers still want those fundamental building blocks and to piece them together themselves, or do they just want AWS to take care of all that? There's no one-size-fits-all solution to what customers want. It is interesting, and I will say somewhat surprising to me, how much basic capabilities, such as price performance of compute, are still absolutely vital to our customers.

But it's absolutely vital. Part of that is because of the size of datasets and because of the machine learning capabilities which are now being created. They require vast amounts of compute, but nobody will be able to do that compute unless we keep dramatically improving the price performance. We also absolutely have more and more customers who want to interact with AWS at a higher level of abstraction…more at the application layer or broader solutions, and we're putting a lot of energy, a lot of resources, into a number of higher-level solutions.

One of the biggest of those … is Amazon Connect, which is our contact center solution. In minutes or hours or days, you can be up and running with a contact center in the cloud. At the beginning of the pandemic, Barclays … sent all their agents home. In something like 10 days, they got 6, agents up and running on Amazon Connect so they could continue servicing their end customers with customer service.

We've built a lot of sophisticated capabilities that are machine learning-based inside of Connect. We can do call transcription, so that supervisors can help with training agents and services that extract meaning and themes out of those calls.

We don't talk about the primitive capabilities that power that, we just talk about the capabilities to transcribe calls and to extract meaning from the calls. It's really important that we provide solutions for customers at all levels of the stack. Given the economic challenges that customers are facing, how is AWS ensuring that enterprises are getting better returns on their cloud investments?

Now's the time to lean into the cloud more than ever, precisely because of the uncertainty. We saw it during the pandemic in early , and we're seeing it again now, which is, the benefits of the cloud only magnify in times of uncertainty.

For example, the one thing which many companies do in challenging economic times is to cut capital expense. For most companies, the cloud represents operating expense, not capital expense. You're not buying servers, you're basically paying per unit of time or unit of storage. That provides tremendous flexibility for many companies who just don't have the CapEx in their budgets to still be able to get important, innovation-driving projects done.

Another huge benefit of the cloud is the flexibility that it provides — the elasticity, the ability to dramatically raise or dramatically shrink the amount of resources that are consumed. You can only imagine if a company was in their own data centers, how hard that would have been to grow that quickly. The ability to dramatically grow or dramatically shrink your IT spend essentially is a unique feature of the cloud.

These kinds of challenging times are exactly when you want to prepare yourself to be the innovators … to reinvigorate and reinvest and drive growth forward again. We've seen so many customers who have prepared themselves, are using AWS, and then when a challenge hits, are actually able to accelerate because they've got competitors who are not as prepared, or there's a new opportunity that they spot. We see a lot of customers actually leaning into their cloud journeys during these uncertain economic times.

Do you still push multi-year contracts, and when there's times like this, do customers have the ability to renegotiate? Many are rapidly accelerating their journey to the cloud. Some customers are doing some belt-tightening. What we see a lot of is folks just being really focused on optimizing their resources, making sure that they're shutting down resources which they're not consuming.

You do see some discretionary projects which are being not canceled, but pushed out. Every customer is free to make that choice. But of course, many of our larger customers want to make longer-term commitments, want to have a deeper relationship with us, want the economics that come with that commitment. We're signing more long-term commitments than ever these days. We provide incredible value for our customers, which is what they care about.

That kind of analysis would not be feasible, you wouldn't even be able to do that for most companies, on their own premises. So some of these workloads just become better, become very powerful cost-savings mechanisms, really only possible with advanced analytics that you can run in the cloud. In other cases, just the fact that we have things like our Graviton processors and … run such large capabilities across multiple customers, our use of resources is so much more efficient than others.

We are of significant enough scale that we, of course, have good purchasing economics of things like bandwidth and energy and so forth.

So, in general, there's significant cost savings by running on AWS, and that's what our customers are focused on. The margins of our business are going to … fluctuate up and down quarter to quarter. It will depend on what capital projects we've spent on that quarter. Obviously, energy prices are high at the moment, and so there are some quarters that are puts, other quarters there are takes.

The important thing for our customers is the value we provide them compared to what they're used to. And those benefits have been dramatic for years, as evidenced by the customers' adoption of AWS and the fact that we're still growing at the rate we are given the size business that we are.

That adoption speaks louder than any other voice. Do you anticipate a higher percentage of customer workloads moving back on premises than you maybe would have three years ago? Absolutely not.

We're a big enough business, if you asked me have you ever seen X, I could probably find one of anything, but the absolute dominant trend is customers dramatically accelerating their move to the cloud.

Moving internal enterprise IT workloads like SAP to the cloud, that's a big trend. See below for more on this. As seen in many of the examples above, there is more than one way to construct a regular expression to achieve the same results. It is possible to write an algorithm that, for two given regular expressions, decides whether the described languages are equal; the algorithm reduces each expression to a minimal deterministic finite state machine , and determines whether they are isomorphic equivalent.

Every regular expression can be written solely in terms of the Kleene star and set unions. This is a surprisingly difficult problem. As simple as the regular expressions are, there is no method to systematically rewrite them to some normal form. The lack of axiom in the past led to the star height problem. In , Dexter Kozen axiomatized regular expressions as a Kleene algebra , using equational and Horn clause axioms.

A regex pattern matches a target string. The pattern is composed of a sequence of atoms. An atom is a single point within the regex pattern which it tries to match to the target string. The simplest atom is a literal, but grouping parts of the pattern to match an atom will require using as metacharacters. Metacharacters help form: atoms ; quantifiers telling how many atoms and whether it is a greedy quantifier or not ; a logical OR character, which offers a set of alternatives, and a logical NOT character, which negates an atom's existence; and backreferences to refer to previous atoms of a completing pattern of atoms.

A match is made, not when all the atoms of the string are matched, but rather when all the pattern atoms in the regex have matched. The idea is to make a small pattern of characters stand for a large number of possible strings, rather than compiling a large list of all the literal possibilities. Depending on the regex processor there are about fourteen metacharacters, characters that may or may not have their literal character meaning, depending on context, or whether they are "escaped", i.

Modern and POSIX extended regexes use metacharacters more often than their literal meaning, so to avoid "backslash-osis" or leaning toothpick syndrome it makes sense to have a metacharacter escape to a literal mode; but starting out, it makes more sense to have the four bracketing metacharacters and { } be primarily literal, and "escape" this usual meaning to become metacharacters.

Common standards implement both. The usual characters that become metacharacters when escaped are dswDSW and N. When entering a regex in a programming language, they may be represented as a usual string literal, hence usually quoted; this is common in C, Java, and Python for instance, where the regex re is entered as "re".

This notation is particularly well known due to its use in Perl , where it forms part of the syntax distinct from normal string literals. In some cases, such as sed and Perl, alternative delimiters can be used to avoid collision with contents, and to avoid having to escape occurrences of the delimiter character in the contents. The IEEE POSIX standard has three sets of compliance: BRE Basic Regular Expressions , [36] ERE Extended Regular Expressions , and SRE Simple Regular Expressions.

SRE is deprecated , [37] in favor of BRE, as both provide backward compatibility. The subsection below covering the character classes applies to both BRE and ERE.

BRE and ERE work together. ERE adds? Furthermore, as long as the POSIX standard syntax for regexes is adhered to, there can be, and often is, additional syntax to serve specific yet POSIX compliant applications. Although POSIX. For example, GNU grep has the following options: " grep -E " for ERE, and " grep -G " for BRE the default , and " grep -P " for Perl regexes.

Perl regexes have become a de facto standard, having a rich and powerful set of atomic expressions. Perl has no "basic" or "extended" levels. As in POSIX EREs, and { } are treated as metacharacters unless escaped; other metacharacters are known to be literal or symbolic based on context alone.

Additional functionality includes lazy matching , backreferences , named capture groups, and recursive patterns. Note that backslash escapes are not allowed. The meaning of metacharacters escaped with a backslash is reversed for some characters in the POSIX Extended Regular Expression ERE syntax.

With this syntax, a backslash causes the metacharacter to be treated as a literal character. POSIX Extended Regular Expressions can often be used with modern Unix utilities by including the command line flag -E. The character class is the most basic regex concept after a literal match. It makes one small sequence of characters match a larger set of characters. Character classes apply to both POSIX levels. When specifying a range of characters, such as [a-Z] i.

lowercase a to uppercase Z , the computer's locale settings determine the contents by the numeric ordering of the character encoding. They could store digits in that sequence, or the ordering could be abc…zABC…Z , or aAbBcC…zZ. So the POSIX standard defines a character class, which will be known by the regex processor installed. Those definitions are in the following table:. POSIX character classes can only be used within bracket expressions.

For example, [[:upper:] ab ] matches the uppercase letters and lowercase "a" and "b". An additional non-POSIX class understood by some tools is [:word:] , which is usually defined as [:alnum:] plus underscore. This reflects the fact that in many programming languages these are the characters that may be used in identifiers. Note that what the POSIX regex standards call character classes are commonly referred to as POSIX character classes in other regex flavors which support them.

With most other regex flavors, the term character class is used to describe what POSIX calls bracket expressions.

Because of its expressive power and relative ease of reading, many other utilities and programming languages have adopted syntax similar to Perl 's — for example, Java , JavaScript , Julia , Python , Ruby , Qt , Microsoft's. NET Framework , and XML Schema. Some languages and tools such as Boost and PHP support multiple regex flavors. Perl-derivative regex implementations are not identical and usually implement a subset of features found in Perl 5. Perl sometimes does incorporate features initially found in other languages.

For example, Perl 5. In Python and some other implementations e. are greedy by default because they match as many characters as possible.

matches the entire line because the entire line begins and ends with a double-quote instead of matching only the first part, "Ganymede,". The aforementioned quantifiers may, however, be made lazy or minimal or reluctant , matching as few characters as possible, by appending a question mark: ". In Java and Python 3. matches the entire line, the regex ".

Thus, possessive quantifiers are most useful with negated character classes, e. Another common extension serving the same function is atomic grouping, which disables backtracking for a parenthesized group. The typical syntax is? Possessive quantifiers are easier to implement than greedy and lazy quantifiers, and are typically more efficient at runtime. Many features found in virtually all modern regular expression libraries provide an expressive power that exceeds the regular languages.

For example, many implementations allow grouping subexpressions with parentheses and recalling the value they match in the same expression backreferences. This means that, among other things, a pattern can match strings of repeated words like "papa" or "WikiWiki", called squares in formal language theory.

The pattern for these strings is. The language of squares is not regular, nor is it context-free , due to the pumping lemma. However, pattern matching with an unbounded number of backreferences, as supported by numerous modern tools, is still context sensitive. However, many tools, libraries, and engines that provide such constructions still use the term regular expression for their patterns. This has led to a nomenclature where the term regular expression has different meanings in formal language theory and pattern matching.

For this reason, some people have taken to using the term regex , regexp , or simply pattern to describe the latter. Larry Wall , author of the Perl programming language, writes in an essay about the design of Raku :. Nevertheless, the term has grown with the capabilities of our pattern matching engines, so I'm not going to try to fight linguistic necessity here. I will, however, generally call them "regexes" or "regexen", when I'm in an Anglo-Saxon mood.

Other features not found in describing regular languages include assertions. Some of them can be simulated in a regular language by treating the surroundings as a part of the language as well. The look-ahead assertions? There are at least three different algorithms that decide whether and how a given regex matches a string.

The oldest and fastest relies on a result in formal language theory that allows every nondeterministic finite automaton NFA to be transformed into a deterministic finite automaton DFA. The DFA can be constructed explicitly and then run on the resulting input string one symbol at a time.

Constructing the DFA for a regular expression of size m has the time and memory cost of O 2 m , but it can be run on a string of size n in time O n. Note that the size of the expression is the size after abbreviations, such as numeric quantifiers, have been expanded. An alternative approach is to simulate the NFA directly, essentially building each DFA state on demand and then discarding it at the next step.

This keeps the DFA implicit and avoids the exponential construction cost, but running cost rises to O mn. The explicit approach is called the DFA algorithm and the implicit approach the NFA algorithm. Adding caching to the NFA algorithm is often called the "lazy DFA" algorithm, or just the DFA algorithm without making a distinction. These algorithms are fast, but using them for recalling grouped subexpressions, lazy quantification, and similar features is tricky.

The third algorithm is to match the pattern against the input string by backtracking. This algorithm is commonly called NFA, but this terminology can be confusing.

This behavior can cause a security problem called Regular expression Denial of Service ReDoS. Although backtracking implementations only give an exponential guarantee in the worst case, they provide much greater flexibility and expressive power. For example, any implementation which allows the use of backreferences, or implements the various extensions introduced by Perl, must include some kind of backtracking.

Some implementations try to provide the best of both algorithms by first running a fast DFA algorithm, and revert to a potentially slower backtracking algorithm only when a backreference is encountered during the match.

GNU grep and the underlying gnulib DFA uses such a strategy. Sublinear runtime algorithms have been achieved using Boyer-Moore BM based algorithms and related DFA optimization techniques such as the reverse scan. Wu agrep , which implements approximate matching, combines the prefiltering into the DFA in BDM backward DAWG matching.

NR-grep's BNDM extends the BDM technique with Shift-Or bit-level parallelism. A few theoretical alternatives to backtracking for backreferences exist, and their "exponents" are tamer in that they are only related to the number of backreferences, a fixed property of some regexp languages such as POSIX. In theoretical terms, any token set can be matched by regular expressions as long as it is pre-defined. In terms of historical implementations, regexes were originally written to use ASCII characters as their token set though regex libraries have supported numerous other character sets.

Many modern regex engines offer at least some support for Unicode. In most respects it makes no difference what the character set is, but some issues do arise when extending regexes to support Unicode.

Regexes are useful in a wide variety of text processing tasks, and more generally string processing , where the data need not be textual.

Common applications include data validation , data scraping especially web scraping , data wrangling , simple parsing , the production of syntax highlighting systems, and many other tasks. While regexes would be useful on Internet search engines , processing them across the entire database could consume excessive computer resources depending on the complexity and design of the regex.

Although in many cases system administrators can run regex-based queries internally, most search engines do not offer regex support to the public. Notable exceptions include Google Code Search and Exalead. However, Google Code Search was shut down in January The specific syntax rules vary depending on the specific implementation, programming language , or library in use. Additionally, the functionality of regex implementations can vary between versions. Because regexes can be difficult to both explain and understand without examples, interactive websites for testing regexes are a useful resource for learning regexes by experimentation.

This section provides a basic description of some of the properties of regexes by way of illustration. The following conventions are used in the examples. Also worth noting is that these regexes are all Perl-like syntax. Standard POSIX regular expressions are different. Unless otherwise indicated, the following examples conform to the Perl programming language, release 5. This means that other implementations may lack support for some parts of the syntax shown here e.

basic vs. The syntax and conventions used in these examples coincide with that of other programming environments as well. Regular expressions can often be created "induced" or "learned" based on a set of example strings.

This is known as the induction of regular languages and is part of the general problem of grammar induction in computational learning theory. Formally, given examples of strings in a regular language, and perhaps also given examples of strings not in that regular language, it is possible to induce a grammar for the language, i. Not all regular languages can be induced in this way see language identification in the limit , but many can.

From Wikipedia, the free encyclopedia. Sequence of characters that forms a search pattern. For the comic book, see Re:Gex. See also: Perl Compatible Regular Expressions.

We matched 'Hel' and 'o W'. There are one or more consecutive letter "l"'s in Hello World. There is an 'H' and a 'e' separated by characters e. The non-greedy match with 'l' followed by one or more characters is 'llo' rather than 'llo Wo'. There is an 'e' followed by zero to many 'l' followed by 'o' e. There exists a substring with at least 1 and at most 2 l's in Hello World. Hello World contains one or more vowels.

Hello World contains at least one of Hello, Hi, or Pogo. There is a word that ends with 'llo'. The space between Hello and World is not alphanumeric. In Hello World there are TWO whitespace characters, which may be separated by other characters. In Hello World there are TWO non-whitespace characters, which may be separated by other characters. There is at least one character in Hello World that is not a digit. Hello World starts with the characters 'He'.

Hello World is a line or string that ends with 'rld'. Hello World is a string that starts with 'H'. Hello World contains a character other than a, b, and c. Main article: Induction of regular languages. Archived from the original on Retrieved The Oxford Handbook of Computational Linguistics. Oxford University Press. ISBN Finite Automata. CRC Press. Archived from the original on 27 February Retrieved 25 July New Mexico State University. Archived from the original PDF on 5 December Retrieved 13 August The concept of regular events was introduced by Kleene via the definition of regular expressions.

Beautiful Code. O'Reilly Media. Retrieved 9 October JIT Compilation Techniques, 2. citing Dennis Ritchie Pattern Matching". Gischer Title unknown Technical Report. Stanford Univ. of Comp.

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We believe in the power of good information to build a brighter future for California. Help support our mission. Mark Baldassare , Dean Bonner , Rachel Lawler , and Deja Thomas. Supported with funding from the Arjay and Frances F. Miller Foundation and the James Irvine Foundation. California voters have now received their mail ballots, and the November 8 general election has entered its final stage.

Amid rising prices and economic uncertainty—as well as deep partisan divisions over social and political issues—Californians are processing a great deal of information to help them choose state constitutional officers and state legislators and to make policy decisions about state propositions. The midterm election also features a closely divided Congress, with the likelihood that a few races in California may determine which party controls the US House.

These are among the key findings of a statewide survey on state and national issues conducted from October 14 to 23 by the Public Policy Institute of California:. Today, there is a wide partisan divide: seven in ten Democrats are optimistic about the direction of the state, while 91 percent of Republicans and 59 percent of independents are pessimistic. Californians are much more pessimistic about the direction of the country than they are about the direction of the state.

Majorities across all demographic groups and partisan groups, as well as across regions, are pessimistic about the direction of the United States. A wide partisan divide exists: most Democrats and independents say their financial situation is about the same as a year ago, while solid majorities of Republicans say they are worse off. Regionally, about half in the San Francisco Bay Area and Los Angeles say they are about the same, while half in the Central Valley say they are worse off; residents elsewhere are divided between being worse off and the same.

The shares saying they are worse off decline as educational attainment increases. Strong majorities across partisan groups feel negatively, but Republicans and independents are much more likely than Democrats to say the economy is in poor shape.

Today, majorities across partisan, demographic, and regional groups say they are following news about the gubernatorial election either very or fairly closely.

In the upcoming November 8 election, there will be seven state propositions for voters. Due to time constraints, our survey only asked about three ballot measures: Propositions 26, 27, and For each, we read the proposition number, ballot, and ballot label. Two of the state ballot measures were also included in the September survey Propositions 27 and 30 , while Proposition 26 was not.

This measure would allow in-person sports betting at racetracks and tribal casinos, requiring that racetracks and casinos offering sports betting make certain payments to the state to support state regulatory costs.

It also allows roulette and dice games at tribal casinos and adds a new way to enforce certain state gambling laws. Fewer than half of likely voters say the outcome of each of these state propositions is very important to them.

Today, 21 percent of likely voters say the outcome of Prop 26 is very important, 31 percent say the outcome of Prop 27 is very important, and 42 percent say the outcome of Prop 30 is very important. Today, when it comes to the importance of the outcome of Prop 26, one in four or fewer across partisan groups say it is very important to them.

About one in three across partisan groups say the outcome of Prop 27 is very important to them. Fewer than half across partisan groups say the outcome of Prop 30 is very important to them.

When asked how they would vote if the election for the US House of Representatives were held today, 56 percent of likely voters say they would vote for or lean toward the Democratic candidate, while 39 percent would vote for or lean toward the Republican candidate.

Democratic candidates are preferred by a point margin in Democratic-held districts, while Republican candidates are preferred by a point margin in Republican-held districts. Abortion is another prominent issue in this election. When asked about the importance of abortion rights, 61 percent of likely voters say the issue is very important in determining their vote for Congress and another 20 percent say it is somewhat important; just 17 percent say it is not too or not at all important.

With the controlling party in Congress hanging in the balance, 51 percent of likely voters say they are extremely or very enthusiastic about voting for Congress this year; another 29 percent are somewhat enthusiastic while 19 percent are either not too or not at all enthusiastic.

Today, Democrats and Republicans have about equal levels of enthusiasm, while independents are much less likely to be extremely or very enthusiastic. As Californians prepare to vote in the upcoming midterm election, fewer than half of adults and likely voters are satisfied with the way democracy is working in the United States—and few are very satisfied.

Satisfaction was higher in our February survey when 53 percent of adults and 48 percent of likely voters were satisfied with democracy in America.

Today, half of Democrats and about four in ten independents are satisfied, compared to about one in five Republicans. Notably, four in ten Republicans are not at all satisfied. In addition to the lack of satisfaction with the way democracy is working, Californians are divided about whether Americans of different political positions can still come together and work out their differences. Forty-nine percent are optimistic, while 46 percent are pessimistic. Today, in a rare moment of bipartisan agreement, about four in ten Democrats, Republicans, and independents are optimistic that Americans of different political views will be able to come together.

Notably, in , half or more across parties, regions, and demographic groups were optimistic. Today, about eight in ten Democrats—compared to about half of independents and about one in ten Republicans—approve of Governor Newsom. Across demographic groups, about half or more approve of how Governor Newsom is handling his job.

Approval of Congress among adults has been below 40 percent for all of after seeing a brief run above 40 percent for all of Democrats are far more likely than Republicans to approve of Congress. Fewer than half across regions and demographic groups approve of Congress.

Approval in March was at 44 percent for adults and 39 percent for likely voters. Across demographic groups, about half or more approve among women, younger adults, African Americans, Asian Americans, and Latinos. Views are similar across education and income groups, with just fewer than half approving. Approval in March was at 41 percent for adults and 36 percent for likely voters. Across regions, approval reaches a majority only in the San Francisco Bay Area.

Across demographic groups, approval reaches a majority only among African Americans. This map highlights the five geographic regions for which we present results; these regions account for approximately 90 percent of the state population. Residents of other geographic areas in gray are included in the results reported for all adults, registered voters, and likely voters, but sample sizes for these less-populous areas are not large enough to report separately.

The PPIC Statewide Survey is directed by Mark Baldassare, president and CEO and survey director at the Public Policy Institute of California. Coauthors of this report include survey analyst Deja Thomas, who was the project manager for this survey; associate survey director and research fellow Dean Bonner; and survey analyst Rachel Lawler. The Californians and Their Government survey is supported with funding from the Arjay and Frances F. Findings in this report are based on a survey of 1, California adult residents, including 1, interviewed on cell phones and interviewed on landline telephones.

The sample included respondents reached by calling back respondents who had previously completed an interview in PPIC Statewide Surveys in the last six months. Interviews took an average of 19 minutes to complete.

Interviewing took place on weekend days and weekday nights from October 14—23, Cell phone interviews were conducted using a computer-generated random sample of cell phone numbers. Additionally, we utilized a registration-based sample RBS of cell phone numbers for adults who are registered to vote in California. All cell phone numbers with California area codes were eligible for selection.

After a cell phone user was reached, the interviewer verified that this person was age 18 or older, a resident of California, and in a safe place to continue the survey e. Cell phone respondents were offered a small reimbursement to help defray the cost of the call. Cell phone interviews were conducted with adults who have cell phone service only and with those who have both cell phone and landline service in the household.

Landline interviews were conducted using a computer-generated random sample of telephone numbers that ensured that both listed and unlisted numbers were called. Additionally, we utilized a registration-based sample RBS of landline phone numbers for adults who are registered to vote in California.

All landline telephone exchanges in California were eligible for selection. For both cell phones and landlines, telephone numbers were called as many as eight times. When no contact with an individual was made, calls to a number were limited to six.

Also, to increase our ability to interview Asian American adults, we made up to three additional calls to phone numbers estimated by Survey Sampling International as likely to be associated with Asian American individuals. Accent on Languages, Inc. The survey sample was closely comparable to the ACS figures. To estimate landline and cell phone service in California, Abt Associates used state-level estimates released by the National Center for Health Statistics—which used data from the National Health Interview Survey NHIS and the ACS.

The estimates for California were then compared against landline and cell phone service reported in this survey. We also used voter registration data from the California Secretary of State to compare the party registration of registered voters in our sample to party registration statewide. The sampling error, taking design effects from weighting into consideration, is ±3. This means that 95 times out of , the results will be within 3. The sampling error for unweighted subgroups is larger: for the 1, registered voters, the sampling error is ±4.

For the sampling errors of additional subgroups, please see the table at the end of this section. Sampling error is only one type of error to which surveys are subject. Results may also be affected by factors such as question wording, question order, and survey timing. We present results for five geographic regions, accounting for approximately 90 percent of the state population.

Residents of other geographic areas are included in the results reported for all adults, registered voters, and likely voters, but sample sizes for these less-populous areas are not large enough to report separately. We also present results for congressional districts currently held by Democrats or Republicans, based on residential zip code and party of the local US House member.

We compare the opinions of those who report they are registered Democrats, registered Republicans, and no party preference or decline-to-state or independent voters; the results for those who say they are registered to vote in other parties are not large enough for separate analysis.

We also analyze the responses of likely voters—so designated per their responses to survey questions about voter registration, previous election participation, intentions to vote this year, attention to election news, and current interest in politics. The percentages presented in the report tables and in the questionnaire may not add to due to rounding.

Additional details about our methodology can be found at www. pdf and are available upon request through surveys ppic. October 14—23, 1, California adult residents; 1, California likely voters English, Spanish. Margin of error ±3.

Republican Sen. The third algorithm is to match the pattern against the input string by backtracking. One misconception is that the judges can't understand this technology — we can. Republicans are far less likely than Democrats and independents to hold this positive view. They are generally well-informed with significant financial backing.

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