Undecidability of the trace coding problem and some decidable cases

Authors:
Michal Kunc
Affiliations:
Department of Mathematics, Masaryk University, Janáckovo nám 2a, 662 95 Brno, Czech Republic
Venue:
Theoretical Computer Science
Year:
2004

Citing 7
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Abstract

We introduce and investigate the notion of weak morphisms of trace monoids with the aim of dealing with the problem of deciding the existence of codings between trace monoids. We prove that this problem is not recursively enumerable, which answers the question raised by Ochmanski in 1988. On the other hand, we show its decidability when restricted to instances with domain monoids defined by acyclic dependence graphs. We also partially answer the question of Diekert from 1990 about the number of free monoids needed for encoding a given trace monoid into their direct product.