# 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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### Is ASM a regular language? [migrated]

I'm giving a presentation where I have a single slide dedicated to formal languages. In this slide I give a simplified overview of the Chomsky Hierarchy and I'd like to give an example of a real world ...
169 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 ...
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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 ...
165 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 ...
183 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 ...
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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 ...
287 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 ...
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### 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 ...
2k 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 ...
311 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. ...
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### 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 ...
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### Is JSON a Regular Language?

I was wondering if the JSON spec defined a regular language. It seems simple enough, but I'm not sure how to prove it myself. The reason I ask, is because I was wondering if one could use regular ...
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### Taxonomy of notable regular expression automata

I'm trying to draw up a taxonomy of algorithms for transforming regular expressions into automata so as to perform some empirical tests of their complexity properties in specific domains. I'm aware ...
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### upper bound on the size of a DFA for A|B given the DFAs for A and B?

Given RegEx A and B where the size of the compiled DFAs are m and ...
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### Is finding the minimum regular expression an NP-complete problem?

I am thinking of the following problem: I want to find a regular expression that matches a particular set of strings (for ex. valid email addresses) and doesn't match others (invalid email addresses). ...
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### Are there “small” machines which can efficiently match regular expressions?

It's well-known that a regular expression can be recognized by a nondeterministic finite automaton of size proportional to the regular expression, or by a deterministic FA which is potentially ...
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### Where do most REGEX implementations fall on the complexity scale?

Most modern implementations of regular expressions, such as the ones in perl or .NET, go beyond the classical computer science definition of REGEXes with features like lookahead and lookbehind. Do ...