Operational Accepting State Complexity: The Unary and Finite Case

Abstract

Let [Formula: see text] be the minimal number of accepting states which is sufficient for deterministic finite automata to accept [Formula: see text]. For a number [Formula: see text] and an [Formula: see text]-ary regularity preserving operation ∘, we define [Formula: see text] as the set of all integers [Formula: see text] such that there are [Formula: see text] languages [Formula: see text], [Formula: see text], with [Formula: see text] In this paper, we study these sets for the operations union, catenation, star, complement, set-subtraction, and intersection where we restrict to unary or finite or unary and finite languages [Formula: see text].