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Sound Structure-Preserving Transformation for Weakly-Left-Linear Deterministic Conditional Term Rewriting Systems

In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is a sound structure-preserving transformation for weakly-left-linear deterministic conditional term rewriting systems. More precisely, we show that every weakly-left-linear deterministic conditional term rewriting system can be converted to an equivalent weakly-left-linear and ultra-weakly-left-linear deterministic conditional term rewriting system and prove that the SR transformation is sound for weakly-left-linear and ultra-weakly-left-linear deterministic conditional term rewriting systems. Here, soundness for a conditional term rewriting system means that reduction of the transformed unconditional term rewriting system creates no undesired reduction sequence for the conditional system.

preprint2017arXivOpen access
Ryota NakayamaNaoki NishidaMasahiko Sakai
Logic in Computer ScienceFormal Languages and Automata Theory
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Ryota NakayamaNaoki NishidaMasahiko Sakai

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