On-line Constraint-based Pattern Matching on Sequences

Abstract

We consider pattern matching problems where patterns are presented as sequences of constraints on input elements. Given an infinite alphabet A, a pattern P is a sequence $\left\langle {{p_{{i_1}}},{p_{{i_2}}},...{p_{{i_m}}}} \right\rangle$ of predicates defined on A. The pattern P matches an input sequence t ∈ A* if t = µ x ₁ x ₂ … x _m v such that p_ij, (x _j ) = true, j = 1, 2,…, m for some µ, v∈A*.

We address the following problem: given a pattern P and an input sequence t, find all positions in t where P matches t. We present an on-line algorithm that solves the problem in general and give an efficient linear-time algorithm for some classes of patterns. The proposed algorithms can be used for efficient on-line pattern matching in digitized presentation of continuous reality such as, for example, digitized images and sounds, or noisy telemetric data.