The Church-Rosser property for ground term-rewriting systems is decidable
Theoretical Computer Science
The reachability and joinability problems for right-ground term-rewriting systems
Journal of Information Processing
Deciding the confluence of ordered term rewrite systems
ACM Transactions on Computational Logic (TOCL)
Deciding Confluence of Certain Term Rewriting Systems in Polynomial Time
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Algorithms and Reductions for Rewriting Problems
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Undecidability of the First Order Theory of One-Step Right Ground Rewriting
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Decision Problems in Ordered Rewriting
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The Confluence of Ground Term Rewrite Systems is Decidable in Polynomial Time
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Reachability and confluence are undecidable for flat term rewriting systems
Information Processing Letters
Classes of term rewrite systems with polynomial confluence problems
ACM Transactions on Computational Logic (TOCL)
Characterizing Confluence by Rewrite Closure and Right Ground Term Rewrite Systems
Applicable Algebra in Engineering, Communication and Computing
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Term rewriting systems provide a versatile model of computation. An important property which allows to abstract from potential nondeterminism of parallel execution of the modelled program is confluence. In this paper we prove that confluence of a fairly large class of systems, namely right ground term rewriting systems, is decidable. We introduce a labelling of variables with colours and constrain substitutions according to these colours. We show how right ground rewriting systems can be reduced to simple systems with coloured variables. Such systems can be analysed using reduction-automata techniques which leads to an interesting decision procedure for confluence.