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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
32 views

Publications on left recursion and PCRE regex engine

Is there any paper (or at least technical report / preprint or even thesis) mentioning that regex engines cannot match expressions that contain "left recursion" (explained below)? I am ...
user avatar
8 votes
1 answer
159 views

Word equations with integer parameters

This is mainly a reference request. Let us define a parameterized expression on a finite alphabet $\Sigma$ as follows: $$e,e':= w\mid w^i \mid e\cdot e'$$ Where $w\in\Sigma^+$ is a word, and $i$ is an ...
user avatar
  • 7,653
0 votes
0 answers
37 views

Regex: Pre-determining the position of matching characters

For all regular expressions, is it possible to pre-determine the set of possible positions in which any given sub-expression may be found? If so, is there any existing research on this subject? Here's ...
user avatar
6 votes
1 answer
157 views

star height of star-free languages

I'm interested in the (restricted) star-height of star free-languages. Recalling the definitions: the star height $h(\mathtt{e})$ of a regular expression $\mathtt{e}$ is $0$ if $\mathtt{e}= \...
user avatar
  • 193
5 votes
1 answer
138 views

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, ...
user avatar
  • 521
10 votes
1 answer
233 views

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 ...
user avatar
  • 7,653
4 votes
0 answers
88 views

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 ...
user avatar
  • 7,653
10 votes
1 answer
749 views

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 ...
user avatar
  • 471
2 votes
0 answers
75 views

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 ...
user avatar
2 votes
1 answer
152 views

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 ...
user avatar
3 votes
2 answers
217 views

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 ...
user avatar
  • 230
3 votes
1 answer
127 views

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^* ...
user avatar
3 votes
1 answer
142 views

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 ...
user avatar
  • 223
7 votes
1 answer
301 views

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 ...
user avatar
  • 193
7 votes
1 answer
468 views

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 ...
user avatar
  • 293
1 vote
0 answers
44 views

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 ...
user avatar
  • 11
9 votes
0 answers
257 views

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 ...
user avatar
6 votes
1 answer
222 views

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 ...
user avatar
  • 223
9 votes
0 answers
217 views

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 ...
user avatar
0 votes
0 answers
28 views

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 ...
user avatar
  • 471
11 votes
1 answer
536 views

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 ...
user avatar
2 votes
0 answers
74 views

Have people explored the problem of regular expressions being matchable? [closed]

I ran into a problem of determining if two regular expressions would have any possible matches in common. For example: Fo*bar and Fo+bar More specifically: if $...
user avatar
5 votes
0 answers
120 views

Salomaa's axiomatisation of regular languages and the use of regular expression in it

I am reading the classical article of A. Salomaa where he gives two axiom systems for regular sets and proofs consistency and completeness. As I have understood it, an axiomatic system in some logic (...
user avatar
  • 1,947
1 vote
0 answers
189 views

Hysteresis in finite automata

The concept of hysteresis seems well suited to describe and distinguish finite automata: "Hysteresis is the dependence of the state of a system on its history." (Wikipedia, Hysteresis) "[The ...
user avatar
15 votes
4 answers
668 views

Hierarchies in regular languages

Is there any known "nice" hierarchy $L_0 \subseteq L_1 \subseteq L_2 \subseteq \dots$ (may be finite) inside the class of regular languages $L$? By nice here, the classes in each hierarchy capture ...
user avatar
21 votes
1 answer
505 views

For which regular expressions $\alpha$ is $\{ \beta \mid L(\alpha) = L(\beta) \}$ PSPACE-complete?

It is well known that the following problem is PSPACE-complete: Given regular expression $\beta$, does $L(\beta) = \Sigma^*$? What about determining equivalence to other (fixed) regular expressions $...
user avatar
  • 2,789
-2 votes
1 answer
221 views

Writing a regular expression for character set $\Sigma = \{a,b,(,)\}$ that not have a parenthesis inside a parenthesis [closed]

Let character set $\Sigma=\{a,b,(,)\}$. I want to write a regular expression for the language $L$ that does not have a parenthesis inside a parenthesis. For example, $(abaab)(bbbaa) \in L$, while $(...
user avatar
  • 1
9 votes
1 answer
949 views

Fully linear time regular expression matching

Is there an $O(n+m)$ algorithm to check whether a size $n$ regular expression matches a size $m$ string, assuming a fixed size alphabet if that matters? The standard NFA algorithm is $O(nm)$ worst ...
user avatar
5 votes
1 answer
3k views

How can one ACTUALLY minimize a regular expression? [closed]

Minimizing regular expressions (in terms of number of symbols) is PSPACE-complete (for example as discussed here: minimizing size of regular expression). But how do you actually do that (i.e., what ...
user avatar
2 votes
0 answers
207 views

Complexity of DBA-recognizable Omega-Languages

Given an $\omega$-regular expression $r$, how difficult is it to decide if $L(r)$ is recognizable by some deterministic Büchi automaton? I know it is solvable in EXPTIME by converting the regular ...
user avatar
  • 153
2 votes
0 answers
331 views

Composition of regular expressions with lookahead into DFAs

Let's say we have a regular expression ("a" | "b"(~!"b"))*, written in Perl or other similar languages that support lookahead, which should match a list of a and b's where b's are not followed by b's. ...
user avatar
  • 366
4 votes
0 answers
89 views

Sub optimal regex equivalence

Regex Equivalence is a hard problem which in general takes exponential space and exponential time. Are there any approximation/sub-optimal algorithms with some theoretical guarantees over equivalence ...
user avatar
  • 141
0 votes
1 answer
60 views

Finding containing sets, within sets of sets

Let $s = \{\sigma_1, \sigma_2 \ldots \sigma_n\}$, where $\sigma_i \in \Sigma$, denote a set of alphabet characters. And $s \in S$ where $S$ denotes a set of sets. Given a new set $s' = \{\sigma'_1, \...
user avatar
0 votes
0 answers
122 views

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 ? ...
user avatar
  • 101
-2 votes
1 answer
376 views

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 ...
user avatar
7 votes
3 answers
759 views

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 ...
user avatar
  • 173
6 votes
3 answers
462 views

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 ...
user avatar
3 votes
1 answer
340 views

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). ...
user avatar
  • 407
16 votes
2 answers
1k views

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 ...
user avatar
  • 4,256
12 votes
1 answer
847 views

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 ...
user avatar
  • 11.7k
14 votes
1 answer
5k views

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, ...
user avatar
8 votes
1 answer
314 views

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 ...
user avatar
0 votes
0 answers
131 views

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 ...
user avatar
30 votes
3 answers
4k views

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 ...
user avatar
  • 1,366
28 votes
1 answer
1k views

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, ...
user avatar
  • 387
4 votes
2 answers
422 views

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 ...
user avatar
  • 143
6 votes
1 answer
279 views

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 ...
user avatar
  • 1,493
9 votes
1 answer
470 views

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 ...
user avatar
  • 1,493
8 votes
1 answer
417 views

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,...
user avatar
  • 211
6 votes
7 answers
2k views

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 ...
user avatar