A Review on State Complexity of Individual Operations

The state complexity of a regular language is the number of states of its minimal determinitisc finite automaton. The complexity of a language operation is the complexity of the resulting language seen as a function of the complexities of the operation arguments. In this report we review some of the results of state complexity of individual operations for regular and some subregular languages. 1 State Complexity and Nondeterministic State Complexity The state complexity of a regular language L, sc(L), is the number of states of its minimal DFA. The nondeterministic state complexity of a regular language L, nsc(L), is the number of states of a minimal NFA that accepts L. Since a DFA is in particular an NFA, for any regular language L one has sc(L) ≤ nsc(L). It is well known that anym-state NFA can be converted, via the subset construction, in an equivalent DFA with at most 2 states [116] (we call this conversion determination). Thus, sc(L) ≤ 2. To show that (i) 0 1 2 · · · m− 2 m− 1 a b a, b a, b a, b a, b

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