Titlebook: Rewriting Techniques and Applications; 19th International C Andrei Voronkov Conference proceedings 2008 Springer-Verlag Berlin Heidelberg 2

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Dependency Pairs for Rewriting with Built-In Numbers and Semantic Data Structures,isets) and contains built-in numbers, thus extending our previous work presented at CADE 2007 [6]. These rewrite systems, which are based on normalized rewriting on constructor terms, allow the specification of algorithms in a natural and elegant way. Built-in numbers are helpful for this since numb

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Arctic Termination ...Below Zero,natural numbers extended with -∞,with the operations ”max” and ”plus”. This extends the matrix method for term rewriting and the arctic matrix method for string rewriting. In combination with the Dependency Pairs transformation, this allows for some conceptually simple termination proofs in cases wh

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Logics and Automata for Totally Ordered Trees,archical and a sequential structure; one example for such data are natural language sentences, where a sequential structure is given by word order, and a hierarchical structure is given by grammatical relations between words. In this paper, we study monadic second-order logic (MSO) for .. We show th

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Diagram Rewriting for Orthogonal Matrices: A Study of Critical Peaks,s structure was introduced by the first author. One of the rules is similar to Yang-Baxter equation. It involves a map . : ]0, .[. →]0, .[...In order to obtain the algebraic properties of ., we study the confluence of critical peaks (or critical pairs) for our rewrite system. For that purpose, we in

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Nominal Unification from a Higher-Order Perspective,c, bound variables are treated as atoms, and only free variables are proper unknowns in nominal unification. This allows “variable capture”, breaking a fundamental principle of lambda-calculus. Despite this difference, nominal unification can be seen from a higher-order perspective. From this view,