Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems

Gmeiner, Karl; Nishida, Naoki

doi:10.4230/oasics.wpte.2014.3

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…[24,28,30,31,33]), mainly to establish (operational) termination and confluence of the input CTRS. The latter originate from Viry [37] and improved versions were proposed in [1,8,13].…”

Section: Discussionmentioning

confidence: 99%

Complexity of Conditional Term Rewriting

Kop¹,

Middeldorp²,

Sternagel³

2017

Logical Methods in Computer Science ; Volume 13

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We propose a notion of complexity for oriented conditional rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that result in a failed rule application. A transformation to unconditional context-sensitive rewrite systems is presented which reflects this complexity notion, as well as a technique to derive runtime and derivational complexity bounds for the result of this transformation.

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“…[24,28,30,31,33]), mainly to establish (operational) termination and confluence of the input CTRS. The latter originate from Viry [37] and improved versions were proposed in [1,8,13].…”

Section: Discussionmentioning

confidence: 99%

Complexity of Conditional Term Rewriting

Kop¹,

Middeldorp²,

Sternagel³

2017

Logical Methods in Computer Science ; Volume 13

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Confluence of Conditional Term Rewrite Systems via Transformations

Gmeiner

2017

Electron. Proc. Theor. Comput. Sci.

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Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term rewrite systems.Recent results provide confluence criteria for conditional term rewrite systems via transformations, yet they are restricted to CTRSs with certain syntactic properties like weak left-linearity. These syntactic properties imply that the transformations are sound for the given CTRS.This paper shows how to use transformations to prove confluence of operationally terminating, right-stable deterministic conditional term rewrite systems without the necessity of soundness restrictions. For this purpose, it is shown that certain rewrite strategies, in particular almost U-eagerness and innermost rewriting, always imply soundness.

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

Nakayama

Nishida

Sakai

2017

Electron. Proc. Theor. Comput. Sci.

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In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Ş erbȃnuţȃ and Roşu, is a sound structure-preserving transformation for weakly-left-linear deterministic conditional term rewriting systems. More precisely, we show that every weakly-leftlinear deterministic conditional term rewriting system can be converted to an equivalent weakly-leftlinear 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.

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Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems

Cited by 4 publications

References 14 publications

Complexity of Conditional Term Rewriting

Complexity of Conditional Term Rewriting

Confluence of Conditional Term Rewrite Systems via Transformations

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

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