# Tagged Questions

Questions about the formal languages that can be described by regular expressions (in the sense of Kleene), or, equivalently, the languages that can be accepted by finite automata.

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### Regular languages from category-theoretical point of view

I noticed that regular languages over the alphabet $\Sigma$ can be naturally thought of as a poset, and indeed a lattice. Moreover, concatenation together with the empty language $\epsilon$ defines a ...
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### Proof that DFA that accepts string has NFA that accepts reversal of string

I have seen descriptions for an algorithm that can take a regular deterministic finite automata and create a non-deterministic finite automata that is guaranteed to generate the reverse of string ...
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### Eilenberg's rational hierarchy of nonrational automata & languages — where is it now?

In the preface to his very influential books Automata, Languages and Machines (Volumes A, B), Samuel Eilenberg tantalizingly promised Volumes C and D dealing with "a hierarchy (called the rational ...
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### What is the minimal extension of FO that captures the class of regular languages?

Context: relations between logic and automata Büchi's Theorem states that Monadic Second Order logic over strings (MSO) captures the class of regular languages. The proof actually shows that ...
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### FSMs with finite memory

Consider an FSM and a finite set of variables. The FSM has the special property that each state contains a set of commands, with each command taking the form of "variable = expr(variable, ...)" e.g., ...
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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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### On the relation for the Myhill-Nerode theorem/syntactic monoid of a language

In order to characterize regular languages one finds the following definition useful: Let $\Sigma$ be an alphabet and $L\subseteq\Sigma^*$. Say that $x,y\in\Sigma^*$ are $\equiv_L$-related, and ...
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### Counting words accepted by a regular grammar

Given a regular language (NFA, DFA, grammar, or regex), how can the number of accepting words in a given language be counted? Both "with exactly n letters" and "with at most n letters" are of ...
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### Complexity lower bound for regular languages

Suppose I have a regular language $L$, and I would like to lower-bound the complexity of deciding membership in $L$. Suppose I know that the minimal DFA for $L$ has $N$ states. I would like to claim ...
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### Number of equivalence classes in regular languages as a function of DFA size

This question is related to a recent question by Janoma. Background In constraint programming, a regular global constraint $c$ over a domain $D$ is a pair $(s, M)$ with $s$ a tuple of variables (...
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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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### algorithm that can determine for every regular language L [closed]

can you please tell me how can I show that there exists an algorithm that can determine for every regular language L, whether or not |L| ≥ 5
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### Ambiguity and Logic

In automata theory (finite automata, pushdown automata, ...) and in complexity, there is a notion of "ambiguity". An automaton is ambiguous if there is a word $w$ with at least two distinct accepting ...