Technical Report: DCC-2013-02

The Operational Incomplete Transition Complexity on Finite Languages

Eva Maia, Nelma Moreira, Rogério Reis

DCC-FC & CMUP, Universidade do Porto
e-mail: {emaia,nam,rvr}
January 2013


The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied 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.