On the state complexity of reversals of regular languages

Authors:
Arto Salomaa;Derick Wood;Sheng Yu
Affiliations:
Turku Centre for Computer Science, Lemminkáisenkatu 14A, 20520 Turku, Finland;Department of Computer Science, Hong kong University of Science and Technology, Clear Water Bay, Kowloon, Hong kong;Department of Computer Science, The University of Western Ontario, Middlesex College 383, Londan, Ont., Canada N6A 5B7
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

We compare the number of states between minimal deterministic finite automata accepting a regular language and its reversal (mirror image). In the worst case the state complexity of the reversal is 2n for an n-state language. We present several classes of languages where this maximal blow-up is actually achieved and study the conditions for it. In the case of finite languages the maximal blow-up is not possible but still a surprising variely of different growth types can be exhibited.