2007/02/07 by Yves Guiraud, Guiraud, Yves
Computer Science · #Category Theory (math.CT) #F.4 #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Model-Driven Software Engineering Techniques
paper · pdf · doi:10.48550/arxiv.cs/0702040
openalex publication_date 2007/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a methodology for proving termination of left-linear term rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of rewriting systems on algebraic circuits. We translate the considered TRS into a polygraph of minimal size whose termination is proven with a polygraphic interpretation, then we get back the property on the TRS. We recall Yves Lafont's general translation of TRSs into polygraphs and known links between their termination properties. We give several conditions on the original TRS, including being a first-order functional program, that ensure that we can reduce the size of the polygraphic translation. We also prove sufficient conditions on the polygraphic interpretations of a minimal translation to imply termination of the original TRS. Examples are given to compare this method with usual polynomial interpretations.