Revisiting Matrix Interpretations for Polynomial Derivational Complexity of Term Rewriting

Neurauter, Friedrich; Zankl, Harald; Middeldorp, Aart

doi:10.1007/978-3-642-16242-8_39

Cited by 26 publications

(31 citation statements)

References 9 publications

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“…As complexity preserving transformations we employ uncurrying [29] for applicative systems whenever it applies and root-labeling [23] in parallel to the base methods. As base methods we use the match-bounds technique as well as TMIs [20,21] and AMIs [16] of dimensions one to five. The latter two are implemented by bit-blasting arithmetic operations to SAT [6].…”

Section: Resultsmentioning

confidence: 99%

“…Recently two approaches were proposed which admit polynomially bounded matrix interpretations going beyond TMIs. While [28] considers weighted automata, in [21] (joint) spectral radius theory is employed. For ease of presentation these criteria have not been considered in this work but since both are based on matrix interpretations, they perfectly suit our modular setting.…”

Section: Resultsmentioning

confidence: 99%

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Modular Complexity Analysis for Term Rewriting

Zankl

Korp

2014

Logical Methods in Computer Science

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Abstract.All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to their restricted power. To overcome this limitation the article introduces a modular framework which allows to infer (polynomial) upper bounds on the complexity of term rewrite systems by combining different criteria. Since the fundamental idea is based on relative rewriting, we study how matrix interpretations and match-bounds can be used and extended to measure complexity for relative rewriting, respectively. The modular framework is proved strictly more powerful than the conventional setting. Furthermore, the results have been implemented and experiments show significant gains in power.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Modular Complexity Analysis for Term Rewriting

Zankl

Korp

2014

Logical Methods in Computer Science

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“…Apart from polynomial interpretations, our reduction pair processor could of course also use matrix interpretations [9,22,24,26,29], polynomial path orders (POP * [3]), etc. For POP * , we would extend C by a complexity Pol * for polytime computability, where Pol n < Pol * < ?…”

Section: Consider the Cpimentioning

confidence: 99%

“…While termination of term rewrite systems (TRSs) is well studied, only recently first results were obtained which adapt termination techniques in order to obtain polynomial complexity bounds automatically, e.g., [2][3][4][5]7,10,[17][18][19][22][23][24]26,29,30]. Here, [3,[17][18][19] consider the dependency pair (DP) method [1,11,12,16], which is one of the most popular termination techniques for TRSs.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Innermost Runtime Complexity of Term Rewriting by Dependency Pairs

Noschinski¹,

Emmes

Giesl

2013

J Autom Reasoning

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We present a modular framework to analyze the innermost runtime complexity of term rewrite systems automatically. Our method is based on the dependency pair framework for termination analysis. In contrast to previous work, we developed a direct adaptation of successful termination techniques from the dependency pair framework in order to use them for complexity analysis. By extensive experimental results, we demonstrate the power of our method compared to existing techniques.

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“…While termination of term rewrite systems (TRSs) is well studied, only recently first results were obtained which adapt termination techniques in order to obtain polynomial complexity bounds automatically, e.g., [2][3][4][5]7,9,15,16,[19][20][21]23,27,28]. Here, [3,15,16] consider the dependency pair (DP) method [1,10,11,14], which is one of the most popular termination techniques for TRSs.…”

Section: Introductionmentioning

confidence: 99%

A Dependency Pair Framework for Innermost Complexity Analysis of Term Rewrite Systems

Noschinski¹,

Emmes²,

Giesl

2011

Lecture Notes in Computer Science

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Abstract. We present a modular framework to analyze the innermost runtime complexity of term rewrite systems automatically. Our method is based on the dependency pair framework for termination analysis. In contrast to previous work, we developed a direct adaptation of successful termination techniques from the dependency pair framework in order to use them for complexity analysis. By extensive experimental results, we demonstrate the power of our method compared to existing techniques.

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Revisiting Matrix Interpretations for Polynomial Derivational Complexity of Term Rewriting

Cited by 26 publications

References 9 publications

Modular Complexity Analysis for Term Rewriting

Modular Complexity Analysis for Term Rewriting

Analyzing Innermost Runtime Complexity of Term Rewriting by Dependency Pairs

A Dependency Pair Framework for Innermost Complexity Analysis of Term Rewrite Systems

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