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On Forward Closure and the Finite Variant Property

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Frontiers of Combining Systems (FroCoS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8152))

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Abstract

Equational unification is an important research area with many applications, such as cryptographic protocol analysis. Unification modulo a convergent term rewrite system is undecidable, even with just a single rule. To identify decidable (and tractable) cases, two paradigms have been developed — Basic Syntactic Mutation [14] and the Finite Variant Property [6]. Inspired by the Basic Syntactic Mutation approach, we investigate the notion of forward closure along with suitable redundancy constraints. We show that a convergent term rewriting system R has a finite forward closure if and only if R has the finite variant property. We also show the undecidability of the finiteness of forward closure, therefore determining if a system has the finite variant property is undecidable.

C. Bouchard, K. Gero, and P. Narendran were supported in part by NSF grant CNS 09-05286. C. Lynch was supported in part by NSF grant CNS 09-05378.

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Bouchard, C., Gero, K.A., Lynch, C., Narendran, P. (2013). On Forward Closure and the Finite Variant Property. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science(), vol 8152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40885-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-40885-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40884-7

  • Online ISBN: 978-3-642-40885-4

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