Asynchronous trace-matching automata

Abstract

This paper presents algorithms for solving several matching problems on Mazurkiewicz traces. The creation of the algorithms is reduced to the construction of automata that recognize corresponding rational trace languages. Such languages and their properties were studied by many authors. This paper considers trace languages used in solving concrete problems that have analogs in stringology.

Forbidden traces and forbidden subtraces

“…This warehouse must be a structure providing the fast search for traces in a set, inclusion of new traces, and change in accompanying information. In [13], a special structure F is proposed for describing sets of traces. This structure is a generalization of prefix trees used to store strings.…”

“…The structure F can be used to store the set of all factors of a trace t and a dictionary of forbidden traces MTF t ( ). The structure F makes it possible to establish (in linear time) the occurrence of a trace in the set w( ) F or to add a new trace [13]. For gathering information on occurrences of each factor s in a trace t, we change the structure of F by adding the possibility of describing neighborhoods of traces to it.…”