Productivity of Non-Orthogonal Term Rewrite Systems

Matthias Raffelsieper
(TU Eindhoven)

Productivity is the property that finite prefixes of an infinite constructor term can be computed using a given term rewrite system. Hitherto, productivity has only been considered for orthogonal systems, where non-determinism is not allowed. This paper presents techniques to also prove productivity of non-orthogonal term rewrite systems. For such systems, it is desired that one does not have to guess the reduction steps to perform, instead any outermost-fair reduction should compute an infinite constructor term in the limit. As a main result, it is shown that for possibly non-orthogonal term rewrite systems this kind of productivity can be concluded from context-sensitive termination. This result can be applied to prove stabilization of digital circuits, as will be illustrated by means of an example.

In Santiago Escobar: Proceedings 10th International Workshop on Reduction Strategies in Rewriting and Programming (WRS 2011), Novi Sad, Serbia, 29 May 2011 , Electronic Proceedings in Theoretical Computer Science 82, pp. 53–67.
Published: 24th April 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.82.4 bibtex PDF
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