# Questions tagged [regular-expressions]

Questions about the theory of regular expressions, both in the sense of Kleene's original definition and of POSIX regular expressions.

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### Regular Expressions that converts into unambiguous automata

Brüggemann-Klein and Wood (1992) proved that a certain kind of regular expressions, that they call “Deterministic Regular expressions”, when converted into automata using the Glushkov's Construction, ...
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### Succinctness of regular expressions with empty word

Consider regular expressions on some alphabet $\Sigma$, without the empty word: $$e,f:=a\in\Sigma\mid e\cdot f \mid e+f\mid e^+$$ These $\varepsilon$⁻free expressions can define all regular languages ...
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### Complexity of inclusion of transfinite expressions

Transfinite expressions on an alphabet $\Sigma$ are generated by the grammar : $$e,f:= a\in\Sigma\mid e\cdot f\mid e+f\mid e^*\mid e^\omega.$$ They describe languages of transfinite words, i.e. words ...
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### Ambiguity of regular expressions

Some regular expressions are ambiguous. Some are not. a*b* is unambiguous for example. Expression a*a* is ambiguous but it can ...
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### Is there a list of notations developed for regular expressions? [closed]

There is, of course, PCRE. I know also of Olin Shiver's Structural Regular Expressions, and Rob Pike's Structural Regular Expressions. I also understand that Raku's regexps are different from perl's ...
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### What graphs on $\mathbb{N}$ can be encoded as regular languages?

Suppose I represent the natural number 0 by "x", and use the symbol "s" for successor so that I get the following encoding of $\alpha : \mathbb{N} \rightarrow V$ of natural numbers ...
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### Match a string agains a set of regexes

There are several algorithms to match a (simple) string against a regular expression (see here). But if we have a lot of regexes, can we find one of them that matches the given string faster than ...
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### Rewrite relations - proof of correctness

Let $T \subseteq \Sigma^* \times \Sigma^*$ be a regular relation. We define the obligatory rewrite relation over $T$ as follows: $$R^{obl}(T) := N(T) \cdot (T \cdot N(T))^*$$  N(T) := Id(\Sigma^* ...
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### Are all RegExp solvable in O(n)?

I'm wondering if all features, that are often part of modern RegEx engines, are solvable in O(n). I'm talking about features like repeating patterns ([abc]+);\1 ...
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### Kleene Algebra for star-free regular expressions

TLDR: Is there a notion of Kleene Algebra for star-free regular expressions? Kleene Algebras are algebraic structures that are equivalent to regular expressions. A Kleene Algebra is an idempotent ...
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### Time complexity of derivative-based regex matchers

Regex matching using the Brzozowski derivative without any caching or expression-simplifying takes exponential time and space because of the product rule. In Brzozowski's original paper, Brzozowski ...
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### Question About Turing Machine Computability [closed]

If p is a Turing machine then L(p) = {x | p(x) = yes}. Let A = {p | p is a Turing machine and L(p) is a finite set}. Is A computable? Justify your answer. So I'm trying to figure out how to solve ...
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### Shortest string in the intersection of regular languages

Inspired by https://codegolf.stackexchange.com/questions/53310/shortest-universal-maze-exit-string Each of the 138,172 valid mazes can be represented as a DFA with 9 states (including starting and ...
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### How powerful is POSIX regex

The set of languages recognized by POSIX regex is a true superset of type 3 languages. But how powerful is POSIX regex really? Is it in an already known class? Is it its own class? If so, what is the ...
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### Regular expressions of prefixes/suffixes

It is well-known that star-free regular expressions, which are defined by the grammar $r::= a \mid r \cdot r \mid r \cup r \mid \neg r \mid \varepsilon \mid \emptyset$ where $a$ belongs to a finite ...
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### Searchable finite field

Let $F$ be a large finite field, where the elements are strings of length $n$. We require, addition, multiplication, and division to be efficient (polynomial in $n$). We say that $F$ is searchable if ...
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### Parameterized complexity of inclusion of regular languages

I am interested in the classic problem REGULAR LANGUAGE INCLUSION. Given a regular expression $E$, we denote by $L(E)$ the regular language associated to it. (Regular expressions are on a fixed ...
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### Is it possible to simulate a regular expression using a single stack?

I understand that a regular expression can be converted to an equivalent DFA which can then be simulated. However, is it possible to simulate the regular expression directly with the aid of a stack ? ...
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### Can I show algebraically that this regular expression accepts all binary strings?

The task is to prove that (0+1)* and 0*(1.0*)* are equivalent. 1. http://rubular.com/r/K9Hp9tU6px 2. http://rubular.com/r/N8VpoEcch4 EDIT: Forgot that + was ambiguous here! I want to prove that the ...
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### Algorithm for ranking members of a regular language?

A little while back, I was reading a paper that mentioned a method for computing an integer 'rank' for a particular string $s \in L$ where $L$ is some regular language. This rank uniquely determines ...
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### Chomsky hierarchy for tree structures

I know of the Chomsky hierarchy, which concerns the expressive power of grammars to recognize languages $L \subseteq \Sigma^*$ made of words on an alphabet $\Sigma$. Is there a similar hierarchy for ...
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### Deterministic Büchi + its complement covers LTL?

It is well known that deterministic Büchi automata (DBA) are less expressive than non-deterministic Büchi automata (NBA), and in particular DBA are not enough to cover linear temporal logic (LTL). ...
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### minimizing size of regular expression for finite sets

It is known that minimizing the size of a regular expression is PSPACE-complete even if we have a DFA as the language's specification. What are the results if the language is finite? One can ...
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### The Cost of an Equivalence Query for DFA

Inspired by this question, I am curious about the following: What is the worst-case complexity of checking whether a given DFA accepts the same language as a given regular expression? Is this ...
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### What algorithms exist for construction a DFA that recognizes the language described by a given regex?

All of my textbooks use the same algorithm for producing a DFA given a regex: First, make an NFA that recognizes the language of the regex, then, using the subset (aka "powerset") construction, ...
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### Regular expressions of families of regular expressions

I was reading about the Star Height Problem and noticed that Eggan's family of regular expressions follows a simple pattern which can be described by a regular expression. My question is: are there ...
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### Given a sequence find the shortest reg exp that generates it?

I'm looking for a way to find the smallest possible regular-expression that accepts a sequence. To make it interesting I don't want any stars(Kleene stars) and preferably no wildcards? For instance ...
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### Known algorithms to go from a DFA to a regular expression

I was wondering whether there is a better'' (I will explain in what sense) algorithm to start from a DFA $\mathcal{A}$ and construct a regular expression $r$ such that $L(\mathcal{A})=L(r)$, than ...
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### Why are regular languages called "regular"?

Why are regular languages (and from that regular expressions) called "regular"? There is lot of regularity also in context-free languages other types of languages. I suppose that, in the beginning, ...
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### Matching regular expressions using regular expressions

Is it possible to create a regular expression that matches regular expressions in any given notation? Or, in other words, does there exist a unambiguous and full notation for regular expressions that ...
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### Regular expressions without union but with backreferences

As a follow-up to my question Regular expressions without alternation, I was wondering what was known about the power of regular expressions in which union is not allowed but backreferences are. I'm ...
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### Regular expressions without alternation

I was wondering about what sets of languages are generated by restrictions of regular expressions. Supposing that all the restrictions have a constant symbol for each element of $\Sigma$ and ...
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### Can regexes containing nongreedy (reluctant) quantifiers be rewritten not to use them?

Consider a regex language with the greedy quantifier $*$, the nongreedy quantifier ${*}?$, ordered alternation, and character classes. (This is essentially a sublanguage of PCRE without backreferences,...
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### What are regular expressions good for?

If you ask a question about parsing HTML with regex, you will certainly be referenced to this famous rant. Though there is not a canonical rant for it, I've also been told that regex aren't powerful ...
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### Is it possible to represent a regular expression with bounded captures using a DFA and O(1) additional processing?

It's well known that a regular expression can be converted to a non-deterministic finite state automaton, which can in turn be converted in to a deterministic finite state automaton. These DFAs can ...
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### Progress on generalized star-height problem?

The (generalized) star height of a language is the minimum nesting of Kleene stars required to represent the language by an extended regular expression. Recall that an extended regular expression over ...
Besides (deterministic) communication complexity $cc(R)$ of a relation $R$, another basic measure for the amount of communication needed is the protocol partition number $pp(R)$. The relation between ...