  A locally threshold testable language L is a language with the property that
for some non negative integers k and l and for some word u from L, a word v
belongs 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 u
and v are either the same or greater than l-1.
  A deterministic finite automaton is called locally threshold testable if the
automaton accepts a locally threshold testable language for some l and k.
  New necessary and sufficient conditions for a deterministic finite automaton
to be locally threshold testable are found. On the basis of these conditions,
we modify the algorithm to verify local threshold testability of the automaton
and to reduce the time complexity of the algorithm. The algorithm is
implemented as a part of the $C/C ^{++}$ package TESTAS.
\texttt{http://www.cs.biu.ac.il/$\sim$trakht/Testas.html}.
