A Polynomial Time Algorithm for Left Right Local Testability

摘要

A right [left] locally testable language S is a language with the property that for some nonnegative integer k two words u and v in alphabet S are equal in the semigroup if (1) the prefix and suffix of the words of length k-1 coincide, (2) the set of segments of length k of the words as well as 3) the order of the first appearance of these segments in prefixes [suffixes] coincide. We present necessary and sufficient condition for graph [semigroup] to be transition graph [semigroup] of the deterministic finite automaton that accepts right [left] locally testable language and necessary and sufficient condition for transition graph of the deterministic finite automaton with locally idempotent semigroup. We introduced polynomial time algorithms for the right [left] local testability problem for transition semigroup and transition graph of the deterministic finite automaton based on these conditions. Polynomial time algorithm verifies transition graph of automaton with locally idempotent transition semigroup.