arXiv subjects

Aart Middeldorp

Publications and source records attributed to Aart Middeldorp.

22 records · Page 2Linked to original sources

arXiv2011

On the Complexity of Deciding Call-by-Need

In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple decidability proofs for classes of rewrite systems that are much larger than earlier classes defined using the complicated sequentiality concept. In this paper we show that we can do without ground tree transducers in order to arrive at decidability proofs that are phrased in direct tree automata constructions. This allows us to derive better complexity bounds.

cs.LO↗

arXiv2011

Uncurrying for Innermost Termination and Derivational Complexity

First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we investigate how this transformation behaves for innermost termination and (innermost) derivational complexity. We prove that it reflects innermost termination and innermost derivational complexity and that it preserves and reflects polynomial derivational complexity. For the preservation of innermost termination and innermost derivational complexity we give counterexamples. Hence uncurrying may be used as a preprocessing transformation for innermost termination proofs and establishing polynomial upper and lower bounds on the derivational complexity. Additionally it may be used to establish upper bounds on the innermost derivational complexity while it neither is sound for proving innermost non-termination nor for obtaining lower bounds on the innermost derivational complexity.

cs.LO↗

arXiv2009

Decreasing Diagrams and Relative Termination

In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further show how to encode the rule-labeling heuristic for decreasing diagrams as a satisfiability problem. Experimental data for both methods are presented.

cs.LO↗

arXiv2007

Satisfying KBO Constraints

This paper presents two new approaches to prove termination of rewrite systems with the Knuth-Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic and the resulting formula is tested for satisfiability. Any satisfying assignment represents a weight function and a precedence such that the induced Knuth-Bendix order orients the rules of the encoded rewrite system from left to right.

cs.SC↗