An Algorithm to Verify Local Threshold Testability of Deterministic Finite Automata

A locally threshold testable language L is a language with the property that for some nonnegative integers k and l, whether or not a word u is in the language L depends on (1) the preex and suux of the word u of length k?1 and (2) the set of intermediate substrings of length k of the word u where the sets of substrings occurring at least j times are the same, for j l. For given k and l the language is called l-threshold k-testable. A nite deterministic automaton is called l-threshold k-testable if the automaton accepts a l-threshold k-testable language. In this paper, the necessary and suucient conditions for an automaton to be locally threshold testable are found. We introduce the rst polynomial time algorithm to verify local threshold testability of the automaton based on this characterization.