Finite automata and unary languages
Theoretical Computer Science
Journal of the ACM (JACM)
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Information Processing Letters
Complexity measures for regular expressions
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Errata to: "finite automata and unary languages"
Theoretical Computer Science
Magic numbers in the state hierarchy of finite automata
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RP'10 Proceedings of the 4th international conference on Reachability problems
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It is well known that any nondeterministic finite automata over a unary alphabet can be represented in a certain normal form called the Chrobak normal form [1]. We present a very simple conversion procedure working in O(n3) time. Then we extend the algorithm to improve two trade-offs concerning conversions between different representations of unary regular languages. Given an n-state NFA, we are able to find a regular expression of size O(n2/log2 n) describing the same language (which improves the previously known O(n2) size bound [8]) and a context-free grammar in Chomsky normal form with O(√n log n) nonterminals (which improves the previously known O(n2/3) bound [3]).