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53
Natural termination
 Theoretical Computer Science
"... Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1 ..."
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Cited by 83 (11 self)
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Abstract. We generalize the various path orderings and the conditions under which they work, and describe an implementation of this general ordering. We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's. 1
Homeomorphic Embedding for Online Termination
 STATIC ANALYSIS. PROCEEDINGS OF SAS’98, LNCS 1503
, 1998
"... Recently wellquasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper, ..."
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Cited by 61 (8 self)
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Recently wellquasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper,
BranchWidth and WellQuasiOrdering in Matroids and Graphs
 J. COMBIN. THEORY SER. B
, 2001
"... We prove that a class of matroids representable over a fixed finite field and with bounded branchwidth is wellquasiordered under taking minors. With some extra work, the result implies Robertson and Seymour's result that graphs with bounded treewidth (or equivalently, bounded branchwidth) are w ..."
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Cited by 38 (9 self)
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We prove that a class of matroids representable over a fixed finite field and with bounded branchwidth is wellquasiordered under taking minors. With some extra work, the result implies Robertson and Seymour's result that graphs with bounded treewidth (or equivalently, bounded branchwidth) are wellquasiordered under taking minors. We will not only derive their result from our result on matroids, but will also use the main tools for a direct proof that graphs with bounded branchwidth are wellquasiordered under taking minors. This proof also provides a model for the proof of the result on matroids, with all specific matroid technicalities strippedoff. 1
Recursive Path Orderings can be ContextSensitive
, 2002
"... Contextsensitive rewriting (CSR) is a simple restriction of rewriting which can be used e.g. for modelling noneager evaluation in programming languages. Many times termination is a crucial property for program verification. Hence, developing tools for automatically proving termination of CSR is ne ..."
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Cited by 29 (21 self)
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Contextsensitive rewriting (CSR) is a simple restriction of rewriting which can be used e.g. for modelling noneager evaluation in programming languages. Many times termination is a crucial property for program verification. Hence, developing tools for automatically proving termination of CSR is necessary. All known methods for...
Constructive Topology and Combinatorics
 In proceeding of the conference Constructivity in Computer Science, San Antonio, LNCS 613
, 1991
"... We present a method to extract constructive proofs from classical arguments proved by topogical means. Typically, this method will apply to the nonconstructive use of compactness in combinatorics, often in the form of the use of König's lemma (which says that a finitely branching tree that is infini ..."
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Cited by 13 (2 self)
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We present a method to extract constructive proofs from classical arguments proved by topogical means. Typically, this method will apply to the nonconstructive use of compactness in combinatorics, often in the form of the use of König's lemma (which says that a finitely branching tree that is infinite has an infinite branch.) The method consists roughly of working with the corresponding pointfree version of the topological argument, which can be proven constructively using only as primitive the notion of inductive definition. We illustrate here this method on the classical "minimal bad sequence" argument used by NashWilliams in his proof of Kruskal's theorem. The proofs we get by this method are wellsuited for mechanisation in interactive proof systems that allow the user to introduce inductively defined notions, such as NuPrl, or MartinLof set theory.
A Constraintbased Partial Evaluator for Functional Logic Programs and its Application
, 1998
"... The aim of this work is the development and application of a partial evaluation procedure for rewritingbased functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewritingbased computational model extends traditional functional ..."
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Cited by 12 (0 self)
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The aim of this work is the development and application of a partial evaluation procedure for rewritingbased functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewritingbased computational model extends traditional functional programming languages by incorporating logical features, including logical variables and builtin search, into its framework. This work is the first to address the automatic specialisation of these functional logic programs. In particular, a theoretical framework for the partial evaluation of rewritingbased functional logic programs is defined and its correctness is established. Then, an algorithm is formalised which incorporates the theoretical framework for the procedure in a fully automatic technique. Constraint solving is used to represent additional information about the terms encountered during the transformation in order to improve the efficiency and size of the residual programs. ...
Long Finite Sequences
, 1998
"... Let k be a positive integer. There is a longest finite sequence x 1 ,...,x n in k letters in which no consecutive block x i ,...,x 2i is a subsequence of any other consecutive block x j ,...,x 2j . Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large ..."
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Cited by 11 (4 self)
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Let k be a positive integer. There is a longest finite sequence x 1 ,...,x n in k letters in which no consecutive block x i ,...,x 2i is a subsequence of any other consecutive block x j ,...,x 2j . Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large. We give a lower bound for n(3) in terms of the familiar Ackerman hierarchy. We also give asymptotic upper and lower bounds for n(k). We view n(3) as a particularly elemental description of an incomprehensibly large integer. Related problems involving binary sequences (two letters) are also addressed. We also report on some recent computer explorations of R. Dougherty which we use to raise the lower bound for n(3).
Simple Termination Revisited
 Proc. 12th International Conference on Automated Deduction, Lecture
, 1994
"... In this paper we investigate the concept of simple termination. A term rewriting system is called simply terminating if its termination can be proved by means of a simplification order. The basic ingredient of a simplification order is the subterm property, but in the literature two different defini ..."
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Cited by 10 (5 self)
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In this paper we investigate the concept of simple termination. A term rewriting system is called simply terminating if its termination can be proved by means of a simplification order. The basic ingredient of a simplification order is the subterm property, but in the literature two different definitions are given: one based on (strict) partial orders and another one based on preorders (or quasiorders). In the first part of the paper we argue that there is no reason to choose the second one, while the first one has certain advantages. Simplification orders are known to be wellfounded orders on terms over a finite signature. This important result no longer holds if we consider infinite signatures. Nevertheless, wellknown simplification orders like the recursive path order are also wellfounded on terms over infinite signatures, provided the underlying precedence is wellfounded. We propose a new definition of simplification order, which coincides with the old one (based on partial or...