Nishida, Naoki and Sakai, Masahiko and Sakabe, Toshiki - Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

lmcs:669 - Logical Methods in Computer Science, August 10, 2012, Volume 8, Issue 3
Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

Authors: Nishida, Naoki and Sakai, Masahiko and Sakabe, Toshiki

Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound w.r.t. reduction for every CTRS, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled TRS is left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling. Finally, we show that soundness of Ohlebusch's unraveling is the weakest in soundness of the other unravelings and a transformation, proposed by Serbanuta and Rosu, for (normal) deterministic CTRSs, i.e., soundness of them respectively implies that of Ohlebusch's unraveling.


Source : oai:arXiv.org:1206.5694
DOI : 10.2168/LMCS-8(3:4)2012
Volume: Volume 8, Issue 3
Published on: August 10, 2012
Submitted on: October 27, 2011
Keywords: Computer Science - Logic in Computer Science,F.4.2


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