Pattern Matching in Trace Monoids.

Jochen Messner

Abstract: An algorithm is presented solving the factor problem in trace monoids. Given two traces represented by words, the algorithm determines in linear time whether the first trace is a factor of the second one. The space used for this task is linear in the length of the first word. Similar to the Knuth-Morris-Pratt Algorithm for the factor problem on words, the algorithm simulates a finite automaton determined by the first word on the second word. To develop the algorithm, we examine overlaps of two traces, and show that they form a lattice. Finally we investigate the lattice of extensible trace pairs (which represent still extensible prefixes of a searched factor appearing in some other trace), because of their close relations to the structures used by the algorithm.