## The state complexities of some basic operations on regular languages.(English)Zbl 0795.68112

Summary: We consider the state complexities of some basic operations on regular languages. We show that the number of states that is sufficiently and necessary in the worst case for a deterministic finite automaton (DFA) to accept the catenation of an $$m$$-state DFA language and an $$n$$-state DFA language is exactly $$m2^ n- 2^{n-1}$$, for $$m,n\geq 1$$. The result of $$2^{n-1}+ 2^{n-2}$$ states is obtained for the star of an $$n$$-state DFA language, $$n>1$$. State complexities for other basic operations and for regular languages over a one-letter alphabet are also studied.

### MSC:

 68Q45 Formal languages and automata 68Q25 Analysis of algorithms and problem complexity
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### References:

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