The word problem for a finite set of ground identities is known to be decidable in polynomial time using congruence closure, and this is also the case if some of the function symbols are assumed to be commutative or defined by certain shallow identities, called strongly shallow. We show that decidability in P is preserved if we add the assumption that certain function symbols f are extensional in the sense that f (s₁, . . . , sn) ≈ f (t₁, . . . , tn) implies s₁ ≈ t₁, . . . , sn ≈ tn. In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:88711 |
| Date | 22 February 2024 |
| Creators | Baader, Franz, Kapur, Deepak |
| Publisher | Springer Science + Business Media B.V. |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 0168-7433, 1573-0670, 10.1007/s10817-022-09624-4, info:eu-repo/grantAgreement/Deutsche Forschungsgemeinschaft/Transregios/389792660//TRR 248: Grundlagen verständlicher Software-Systeme - für eine nachvollziehbare cyber-physische Welt, info:eu-repo/grantAgreement/National Science Foundation/Directorate for Computer & Information Science & Engineering | Division of Computing and Communication Foundations/1908804//AF: Small: Comprehensive Groebner, Parametric GCD Computations and Real Geometric Reasoning |
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