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A locally threshold testable language L is a language with the property thatfor some non negative integers k and l and for some word u from L, a word vbelongs to L if and only if  (1) the prefixes [suffixes] of length k-1 of words u and v coincide,  (2) the numbers of occurrences of every factor of length k in both words uand v are either the same or greater than l-1.  A deterministic finite automaton is called locally threshold testable if theautomaton accepts a locally threshold testable language for some l and k.  New necessary and sufficient conditions for a deterministic finite automatonto be locally threshold testable are found. On the basis of these conditions,we modify the algorithm to verify local threshold testability of the automatonand to reduce the time complexity of the algorithm. The algorithm isimplemented as a part of the $C/C ^{++}$ package TESTAS.\texttt{http://www.cs.biu.ac.il/$\sim$trakht/Testas.html}.

Reducing the time complexity of testing for local threshold testability