2021-12-09T08:19:37Zhttps://kitami-it.repo.nii.ac.jp/oaioai:kitami-it.repo.nii.ac.jp:000079522021-09-07T05:08:26Z1PROOF OF UNSATISFIABILITY OF ATOM SETS BASED ON COMPUTATION BY EQUIVALENT TRANSFORMATION RULESMiura, KatsunoriAkama, KiyoshiKoike, HidekatsuMabuchi, HiroshiUnsatisabilityProofEquivalent transformation ruleInductionEquivalent Transformation (ET) rules can be used to construct correct se-\nquential and parallel programs, as they are inherently correct. One important method\nfor making ET rules uses logical formulas. Among logical formulas, unsatis able con-\njunctions of nite atoms, each of which is represented by an atom set in this paper, are\nespecially useful for making many ET rules that are used for constructing efficient pro-\ngrams. This paper proposes a method of proving unsatis ability of an atom set based on\ncomputation by ET rules. The proposed method is recursive, in the sense that, during\nproving the given atom set, it may nd a new atom set based on subset relation or in-\nductive structure. Since our proposed method incorporates search based on subset and\ninductive relations, it can be used to prove unsatis ability of various atom sets that can-\nnot be proven by conventional methods.journal articleICIC International2013-11application/pdfInternational Journal of Innovative Computing, Information and Control11944194430https://kitami-it.repo.nii.ac.jp/record/7952/files/2013.11_Proof of Unsatisfiability of Atom Sets based on Computation by Equivalent Transformation Rules.pdfengc 2013 ICIC International