View metadata, citation and similar papers at core.ac.uk brought to you by CORE Information and Computation 170, 1–25 (2001) doi:10.1006/inco.2001.3055, available online at http://www.idealibrary.com on provided by Elsevier - Publisher Connector Confluence Problems for Trace Rewriting Systems Markus Lohrey Institut fur¨ Informatik, Universitat¨ Stuttgart, Breitwiesenstr. 20–22, 70565 Stuttgart, Germany E-mail:
[email protected] Received September 18, 1997; revised; published online Rewriting systems over trace monoids, briefly trace rewriting systems, generalize both semi-Thue systems and vector replacement systems. In [21], a particular trace monoid M is presented such that confluence is undecidable for the class of length–reducing trace rewriting systems over M. In this paper, we show that this result holds for every trace monoid, which is neither free nor free commutative. Furthermore we show that confluence for special trace rewriting systems over a fixed trace monoid is decidable in polynomial time. C 2001 Academic Press Key Words: confluence; trace monoids; undecidability results. 1. INTRODUCTION The theory of free partially commutative monoids generalizes both the theory of free monoids and the theory of free commutative monoids. In computer science, free partially commutative monoids are commonly called trace monoids and their elements are called traces. Both notions are due to Mazurkiewicz [20], who recognized traces as a model of concurrent processes. [14] gives an extensive overview about current research trends in trace theory. The relevance of trace theory for computer science can be explained as follows. Assume a finite alphabet 6. An element of the free monoid over 6, i.e., a finite word over 6, may be viewed as the sequence of actions of a sequential process.