Abstract

We improve the upper bound on the order of local testability of a locally testable deterministic finite automaton with n states to n2\Gamma n 2 + 1. This bound is the best possible.We give an answer to the following conjecture of Kim, McNaughton and McCloskey for deterministic finite locally testable automata with n states: "Is the order of local testability no greater than O(n1:5) when the alphabet size is two?" Our answer is negative. In the case of size two the situation is the same as in general case: the order of local testability is \Omega (n2).

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