An efficient algorithm for order evaluation of Strict Locally Testable languages

Abstract

Strict k-local testability is an important concept in fields like pattern recognition, neural networks and formal languages theory. Words of a strict k-locally testable language L are parsed by decomposing the input in k-length sub strings without the need to consider context-dependent phenomena. First, we study the problem to decide if a language L is strict locally testable: an algorithm is presented to ascertain whether a value of k exists such that L is k-locally testable in a strict sense. Then we face the problem to determine the order of language L, e.g. the minimum value of parameter k so that string recognition can be optimally performed. Our approach relies on the development of the concept of a prefix path intersection graph. Through it, we can provide topological characterizations of strict local testability properties that can efficiently be tested in polynomial time. Moreover, the methods proposed in this paper distinguish from previously achieved results because we do no..