Termination Proofs by Context-Dependent Interpretations

Hofbauer, Dieter

doi:10.1007/3-540-45127-7_10

Cited by 20 publications

(46 citation statements)

References 16 publications

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“…is not well-founded for any m ∈ R. However, as in [10], given δ ∈ R >0 , we use the following (strict) ordering on the set of real numbers:…”

Section: We Can Define An Ordering > On Terms Given By T > S If and Omentioning

confidence: 99%

Polynomials for Proving Termination of Context-Sensitive Rewriting

Lucas

2004

Lecture Notes in Computer Science

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Abstract. We show how to generate well-founded and stable term orderings based on polynomial interpretations over the real numbers. Monotonicity (another usual requirement in termination proofs) can, then, be gradually introduced in the interpretations to deal with different applications. For instance, the dependency pairs method for proving termination of rewriting, and some restrictions of the rewrite relation which are not monotonic in all arguments of the function symbols, can benefit from this approach. The latter is the case for context-sensitive rewriting (CSR), a simple restriction of rewriting which has been proved useful for describing the semantics of several programming languages (e.g., Maude) and analyzing the properties of the corresponding programs. We show how to automatically generate polynomial interpretations over the real numbers for proving termination of CSR.

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“…is not well-founded for any m ∈ R. However, as in [10], given δ ∈ R >0 , we use the following (strict) ordering on the set of real numbers:…”

Section: We Can Define An Ordering > On Terms Given By T > S If and Omentioning

confidence: 99%

Polynomials for Proving Termination of Context-Sensitive Rewriting

Lucas

2004

Lecture Notes in Computer Science

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“…On the practical side, we design an algorithm that automatically searches for ∆-linear interpretations and ∆-restricted interpretations, which shows that the technique can be mechanised. This answers a question posed by Hofbauer in [7]. The procedure has been implemented and we provide ample numerical data to assess its viability.…”

Section: Introductionmentioning

confidence: 85%

“…In particular polynomial interpretations typically overestimate the derivational complexity. In [7] Hofbauer introduced socalled context dependent interpretations as a remedy. These interpretations extend traditional interpretations by introducing an additional parameter.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore this technique allows the handling of non-simple terminating systems. (See [7] and Section 2 for further details. )…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, we provide examples showing that these bounds are tight. In [7] it is shown that context dependent interpretations are expressive enough to show termination of TRSs that are not simply terminating. We improve upon this and show that ∆-restricted interpretations suffice here.…”

Section: Introductionmentioning

confidence: 99%

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Proving Quadratic Derivational Complexities Using Context Dependent Interpretations

Moser

Schnabl

Rewriting Techniques and Applications

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Abstract. In this paper we study context dependent interpretations, a semantic termination method extending interpretations over the natural numbers, introduced by Hofbauer. We present two subclasses of context dependent interpretations and establish tight upper bounds on the induced derivational complexities. In particular we delineate a class of interpretations that induces quadratic derivational complexity. Furthermore, we present an algorithm for mechanically proving termination of rewrite systems with context dependent interpretations. This algorithm has been implemented and we present ample numerical data for the assessment of the viability of the method.

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Derivational Complexity of Knuth-Bendix Orders Revisited

Moser

2006

Logic for Programming, Artificial Intelligence, and Reasoning

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Termination Proofs by Context-Dependent Interpretations

Cited by 20 publications

References 16 publications

Polynomials for Proving Termination of Context-Sensitive Rewriting

Polynomials for Proving Termination of Context-Sensitive Rewriting

Proving Quadratic Derivational Complexities Using Context Dependent Interpretations

Derivational Complexity of Knuth-Bendix Orders Revisited

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