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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/9892

Title: Reducibility of operation symbols in term rewriting systems and its application to behavioral specifications
Authors: Nakamura, Masaki
Ogata, Kazuhiro
Futatsugi, Kokichi
Keywords: Term rewriting system
Algebraic specification
Behavioral specification
Behavioral coherence
Observational transition system
Issue Date: 2010-02-01
Publisher: Elsevier
Magazine name: Journal of Symbolic Computation
Volume: 45
Number: 5
Start page: 551
End page: 573
DOI: 10.1016/j.jsc.2010.01.008
Abstract: In this paper, we propose the notion of reducibility of symbols in term rewriting systems (TRSs). For a given algebraic specification, operation symbols can be classified on the basis of their denotations: the operation symbols for functions and those for constructors. In a model, each term constructed by using only constructors should denote an element, and functions are defined on sets formed by these elements. A term rewriting system provides operational semantics to an algebraic specification. Given a TRS, a term is called reducible if some rewrite rule can be applied to it. An irreducible term can be regarded as an answer in a sense. In this paper, we define the reducibility of operation symbols as follows: an operation symbol is reducible if any term containing the operation symbol is reducible. Non-trivial properties of context-sensitive rewriting, which is a simple restriction of rewriting, can be obtained by restricting the terms on the basis of variable occurrences, its sort, etc. We confirm the usefulness of the reducibility of operation symbols by applying them to behavioral specifications for proving the behavioral coherence property.
Rights: NOTICE: This is the author's version of a work accepted for publication by Elsevier. Masaki Nakamura, Kazuhiro Ogata, Kokichi Futatsugi, Journal of Symbolic Computation, 45(5), 2010, 551-573, http://dx.doi.org/10.1016/j.jsc.2010.01.008
URI: http://hdl.handle.net/10119/9892
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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