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Title:Sufficient Completeness Checking with Propositional Tree Automata
Author(s):Hendrix, Joe; Ohsaki, Hitoshi; Meseguer, José
Subject(s):computer science
Abstract:Sufficient completeness means that enough equations have been specified, so that the functions of an equational specification are fully defined on all relevant data. This is important for both debugging and formal reasoning. In this work we extend sufficient completeness methods to handle expressive specifications involving: (i) partiality; (ii) conditional equations; and (iii) deduction modulo axioms. Specifically, we give useful characterizations of the sufficient completeness property for membership equational logic (MEL) specifications having features (i)--(iii). We also propose a kind of equational tree automata, called propositional tree automata (PTA) and identify a class of MEL specifications (called PTA-checkable) whose sufficient completeness problem is equivalent to the emptiness problem of their associated PTA. When the reasoning modulo involves only symbols that are either associative and commutative (AC) or free, we further show that the emptiness of AC-PTA is decidable, and therefore that the sufficient completeness of AC-PTA-checkable specifications is decidable. The methods presented here can serve as a basis for building a next-generation sufficient completeness tool for MEL specifications having features (i)--(iii). These features are widely used in practice, and are supported by languages such as Maude and other advanced specification and equational programming languages.
Issue Date:2005-09
Genre:Technical Report
Other Identifier(s):UIUCDCS-R-2005-2635
Rights Information:You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS:2009-04-20

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