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.
57
questions
10
votes
1answer
212 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 ...
4
votes
0answers
84 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 ...
10
votes
1answer
715 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 ...
2
votes
0answers
66 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 ...
2
votes
1answer
143 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 ...
3
votes
2answers
178 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 ...
3
votes
1answer
119 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^* ...
3
votes
1answer
141 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 ...
7
votes
1answer
272 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 ...
6
votes
1answer
387 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 ...
1
vote
0answers
42 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 ...
9
votes
0answers
212 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 ...
6
votes
1answer
189 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 ...
9
votes
0answers
213 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 ...
0
votes
0answers
27 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 ...
11
votes
1answer
456 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 ...
2
votes
0answers
73 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 $...
5
votes
0answers
110 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 (...
1
vote
0answers
183 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 ...
15
votes
4answers
645 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 ...
21
votes
1answer
473 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 $...
-2
votes
1answer
216 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 $(...
9
votes
1answer
812 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 ...
5
votes
1answer
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 ...
2
votes
0answers
205 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 ...
2
votes
0answers
323 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.
...
4
votes
0answers
86 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 ...
0
votes
1answer
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, \...
0
votes
0answers
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 ? ...
-2
votes
1answer
369 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 ...
7
votes
3answers
724 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 ...
6
votes
3answers
444 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 ...
3
votes
1answer
314 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). ...
15
votes
2answers
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 ...
12
votes
1answer
797 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 ...
12
votes
1answer
4k 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, ...
8
votes
1answer
285 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 ...
0
votes
0answers
125 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 ...
30
votes
3answers
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 ...
27
votes
1answer
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, ...
4
votes
2answers
405 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 ...
6
votes
1answer
260 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 ...
9
votes
1answer
453 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 ...
8
votes
1answer
408 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,...
6
votes
7answers
1k 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 ...
5
votes
5answers
777 views
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 ...
15
votes
3answers
826 views
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 ...
4
votes
1answer
2k views
Regular expressions: Finding “negation” of regular expression?
Given regular expressions containing only (,),|,* and characters of an Alphabet A, how can I find the "negation" of a regular expression i.e.:
...
22
votes
2answers
1k views
Protocol partition number and deterministic communication complexity
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 ...
19
votes
2answers
6k views
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 ...
