Incomplete transition complexity of basic operations on finite languages

Authors:
Eva Maia;Nelma Moreira;Rogério Reis
Affiliations:
CMUP & DCC, Faculdade de Ciências da Universidade do Porto, Porto, Portugal;CMUP & DCC, Faculdade de Ciências da Universidade do Porto, Porto, Portugal;CMUP & DCC, Faculdade de Ciências da Universidade do Porto, Porto, Portugal
Venue:
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Year:
2013

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Abstract

The state complexity of basic operations on finite languages (considering complete DFAs) has been extensively studied in the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of boolean operations, concatenation, star, and reversal. For all operations we give tight upper bounds for both descriptional measures. We correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right automaton is larger than the left one. For all binary operations the tightness is proved using family languages with a variable alphabet size. In general the operational complexities depend not only on the complexities of the operands but also on other refined measures.