Modular Complexity Analysis for Term Rewriting

Zankl, Harald; Korp, Martin

doi:10.2168/lmcs-10(1:19)2014

Cited by 15 publications

(9 citation statements)

References 26 publications

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“…Nowadays, it can also be used for other properties of TRSs, e.g., confluence, complexity, and completion (where it has to be checked for a given TRS R and equational system E , whether R is a convergent TRS that is equivalent to E ). As a result, there are several tools which support CPF, namely the termination tools AProVE [12], Ci ME [6], Matchbox [29], and T T T 2 [19]; the complexity tools C a T [32] and T C T [3]; the confluence tool CSI [31]; and the completion tools KBCV [25] and mkbTT [30]. CPF is an XML format.…”

Section: The Certification Problem Formatmentioning

confidence: 99%

The Certification Problem Format

Sternagel

Thiemann

2014

Electron. Proc. Theor. Comput. Sci.

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We provide an overview of CPF, the certification problem format, and explain some design decisions. Whereas CPF was originally invented to combine three different formats for termination proofs into a single one, in the meanwhile proofs for several other properties of term rewrite systems are also expressible: like confluence, complexity, and completion. As a consequence, the format is already supported by several tools and certifiers. Its acceptance is also demonstrated in international competitions: the certified tracks of both the termination and the confluence competition utilized CPF as exchange format between automated tools and trusted certifiers.

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Section: The Certification Problem Formatmentioning

confidence: 99%

The Certification Problem Format

Sternagel

Thiemann

2014

Electron. Proc. Theor. Comput. Sci.

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“…While complexity analysis of term rewriting is well studied (e.g., [3,4,5,6,7,9,11,13,15,16,17,18,19,20,21,22,26]), the results of the annual Termination Competition [24] show that automatic techniques to infer upper bounds for rc are still substantially weaker than corresponding techniques for irc. 899 examples were analyzed for both rc and irc at the Termination Competitions 2015 and 2016.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Runtime Complexity via Innermost Runtime Complexity

Frohn

Giesl

EPiC Series in Computing

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There exist powerful techniques to infer upper bounds on the innermost runtime complexity of term rewrite systems (TRSs), i.e., on the lengths of rewrite sequences that follow an innermost evaluation strategy. However, the techniques to analyze the (full) runtime complexity of TRSs are substantially weaker. In this paper, we present a sufficient criterion to ensure that the runtime complexity of a TRS coincides with its innermost runtime complexity. This criterion can easily be checked automatically and it allows us to use all techniques and tools for innermost runtime complexity in order to analyze (full) runtime complexity. By extensive experiments with an implementation of our results in the tool AProVE, we show that this improves the state of the art of automated complexity analysis significantly.

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“…The continuing development of automated termination and complexity analysers for both first-and higher-order term rewriting systems echoes the immense practical, and hence also theoretical, demand for complexity analysis frameworks of declarative programming languages, see e.g. [GBE + 14,ZK14].…”

Section: Introductionmentioning

confidence: 99%

Combinatorics of Explicit Substitutions

Bendkowski

Lescanne

2018

Proceedings of the 20th International Symposium on Principles and Practice of Declarative Programming

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λυ is an extension of the λ-calculus which internalises the calculus of substitutions. In the current paper, we investigate the combinatorial properties of λυ focusing on the quantitative aspects of substitution resolution. We exhibit an unexpected correspondence between the counting sequence for λυ-terms and famous Catalan numbers. As a by-product, we establish effective sampling schemes for random λυ-terms. We show that typical λυ-terms represent, in a strong sense, non-strict computations in the classic λ-calculus. Moreover, typically almost all substitutions are in fact suspended, i.e. unevaluated, under closures. Consequently, we argue that λυ is an intrinsically non-strict calculus of explicit substitutions. Finally, we investigate the distribution of various redexes governing the substitution resolution in λυ and investigate the quantitative contribution of various substitution primitives.

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Modular Complexity Analysis for Term Rewriting

Cited by 15 publications

References 26 publications

The Certification Problem Format

The Certification Problem Format

Analyzing Runtime Complexity via Innermost Runtime Complexity

Combinatorics of Explicit Substitutions

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