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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.

8 votes

Complexity of intersection of regular languages as context-free grammars

This is a great question and it really lies within my interests. I'm glad that you asked it Max. Let $n$ DFA's with at most $O(n)$ states each be given. It would be nice if there existed a PDA with …
Michael Wehar's user avatar
26 votes
Accepted

Deciding emptiness of intersection of regular languages in subquadratic time

Simple answer: If there does exist a more efficient algorithm that runs in $O(n^{\delta})$ time for some $\delta < 2$, then the strong exponential time hypothesis would be refuted. We will prove a …
Michael Wehar's user avatar
4 votes
Accepted

DFSA and NFSA intersection problem

Regarding question (1): As long as $k$ is $\Omega(n^c)$ for some $c > 0$, then the problem is $PSPACE$-complete. See this paper by Klaus-Jörn Lange and Peter Rossmanith (1992) for some related result …
Michael Wehar's user avatar