The state complexities of some basic operations on regular languages
Theoretical Computer Science
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On the state complexity of reversals of regular languages
Theoretical Computer Science
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On a structural property in the state complexity of projected regular languages
Theoretical Computer Science
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We study the state complexity of the reverse of acyclic minimal deterministic finite automata, and the computational complexity of the following problem: Given an acyclic minimal DFA, is the minimal DFA for the reverse also acyclic? Note that we allow self-loops in acyclic automata. We show that there exists a language accepted by an acyclic minimal DFA such that the minimal DFA for its reverse is exponential with respect to the number of states, and we establish a tight bound on the state complexity of the reverse of acyclic DFAs. We also give a direct proof of the fact that the minimal DFA for the reverse is acyclic if and only if the original acyclic minimal DFA satisfies a certain structural property, which can be tested in quadratic time.