Incomplete Transition Complexity of Basic Operations on Finite Languages

Abstract

Abstract. 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.

Incomplete operational transition complexity of regular languages

“…Note that the values in the table are obtained using languages for which the upper bounds are reached. This paper expands the work presented in extended abstracts [16,15] with full proofs of theorems and experimental tests.…”

From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

“…A partial DFA cannot save more than one state compared to an ordinary DFA, but it can save a considerable number of transitions in some cases. This phenomenon is studied, e.g., in [30,75,76]. Further measures for the complexity of finite automata, in particular measures related to unambiguity and limited nondeterminism, can be found in [39,40,41,59,63,70,71,72,92,93,95].…”