LIPIcs.FSCD.2016.22.pdf
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Non-Omega-Overlapping TRSs are UN
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1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Formal Structures for Computation and Deduction (FSCD) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2016-06-17
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Stefan Kahrs and Connor Smith. Non-Omega-Overlapping TRSs are UN. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.FSCD.2016.22
https://doi.org/10.4230/LIPIcs.FSCD.2016.22
Abstract
This paper solves problem #79 of RTA's list of open
problems --- in the positive. If the rules of a TRS do not overlap w.r.t.
substitutions of infinite terms then the TRS has unique normal forms.
We solve the problem by reducing the problem to one of consistency for
"similar" constructor term rewriting systems. For this we introduce
a new proof technique. We define a relation ⇓ that is
consistent by construction, and which --- if transitive --- would
coincide with the rewrite system's equivalence relation =R.
We then prove the transitivity of ⇓ by coalgebraic
reasoning. Any concrete proof for instances of this relation only
refers to terms of some finite coalgebra, and we then construct an
equivalence relation on that coalgebra which coincides with ⇓.
Keywords
- consistency
- omega-substitutions
- uniqueness of normal forms
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