Algorithms and reductions for rewriting problems [chapter]

Rakesh M. Verma, Michael Rusinowitch, Denis Lugiez
1998 Lecture Notes in Computer Science  
In this paper we initiate a study of polynomial-time reductions for some basic decision problems of rewrite systems. We then give a polynomial-time algorithm for Unique-normal-form property of ground systems for the rst time. Next we prove undecidability of these problems for a xed string rewriting system using our reductions. Finally, we prove partial decidability results for Con uence of commutative semi-thue systems. The Con uence and Unique-normal-form property are shown Expspace-hard for
more » ... mmutative semi-thue systems. We also show that there is a family of string rewrite systems for which the word problem is trivially decidable but con uence undecidable, and we show a linear equational theory with decidable word problem but undecidable linear equational matching.
doi:10.1007/bfb0052369 fatcat:a4jqeyr33ve7jpkcunin6vdg6q