Productivity of Non-Orthogonal Term Rewrite Systems

Details Productivity of Non-Orthogonal Term Rewrite Systems Productivity of Non-Orthogonal Term Rewrite Systems

2012-04-25

arxiv.org/abs/1204.5544v1

EPTCS 82, 2012, pp. 53-67

Computer Science

Logic in Computer Science

In Proceedings WRS 2011, arXiv:1204.5318

Scientific paper

10.4204/EPTCS.82.4

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.

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