A new algorithm for testing if a regular language is locally threshold testable

A new algorithm is presented for testing if a regular language is locally threshold testable. The new algorithm is slower than existing algorithms, but its correctness proof is shorter. The proof idea is to restate the problem in Presburger arithmetic. Key words: Formal Languages A language L ⊆ A∗ is called locally threshold testable (LTT) if it is a Boolean combination of languages of the form: a) words that have w ∈ A∗ as a prefix; or b) words that have w ∈ A∗ as a suffix; or c) words that have w ∈ A∗ as an infix at least n times. For instance, the language a+ b+ a+ b+ is locally threshold testable, as witnessed by: “words that have a as a prefix, have ab as an infix exactly two times, and have ba as an infix exactly one time”. By Gaifman’s theorem, locally threshold testable is equivalent to being definable in first-order logic with the successor relation on positions. This paper presents a new proof of the following theorem: Theorem 1 It is decidable i...

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Mikolaj Bojanczyk
• Keywords: Algorithm, IPL 2007, Regular Language, Testable