Complexity, Graphs, and the Dependency Pair Method

Hirokawa, Nao; Moser, Georg

doi:10.1007/978-3-540-89439-1_45

Cited by 15 publications

(43 citation statements)

References 10 publications

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“…Since DTs represent several DPs, we now obtain chain trees. (This is analogous to the path detection in [16]). …”

Section: Definition 4 (Dependency Tuple)mentioning

confidence: 91%

“…While DPs are used for termination, for complexity we have to regard all defined functions in a right-hand side at once. Thus, we extend the concept of weak dependency pairs [15,16] and only build a single dependency tuple → [r| π1 , . .…”

Section: Dependency Tuplesmentioning

confidence: 99%

“…Note that DTs are much closer to the original DP method than the weak DPs of [15,16]. While weak DPs also use compound symbols, they only consider the topmost defined function symbols in right-hand sides of rules.…”

Section: Definition 4 (Dependency Tuple)mentioning

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]7,9,15,16,[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. 3 Moreover, [28] introduces a related modular approach for complexity analysis based on relative rewriting.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to [3,15,16], we follow the original DP framework closely. This allows us to directly adapt the several termination techniques ("processors") of the DP framework for complexity analysis.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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“…Since DTs represent several DPs, we now obtain chain trees. (This is analogous to the path detection in [16]). …”

Section: Definition 4 (Dependency Tuple)mentioning

confidence: 91%

Section: Dependency Tuplesmentioning

confidence: 99%

Section: Definition 4 (Dependency Tuple)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Automated Complexity Analysis Based on the Dependency Pair Method

Hirokawa

Moser

Automated Reasoning

Self Cite

164

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Abstract. In this paper, we present a variant of the dependency pair method for analysing runtime complexities of term rewrite systems automatically. This method is easy to implement, but signicantly extends the analytic power of existing direct methods. Our ndings extend the class of TRSs whose linear or quadratic runtime complexity can be detected automatically. We provide ample numerical data for assessing the viability of the method.

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The Derivational Complexity Induced by the Dependency Pair Method

Moser

Schnabl

2009

Rewriting Techniques and Applications

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Abstract. We study the derivational complexity induced by the dependency pair method, enhanced with standard refinements. We obtain upper bounds on the derivational complexity induced by the dependency pair method in terms of the derivational complexity of the base techniques employed. In particular we show that the derivational complexity induced by the dependency pair method based on some direct technique, possibly refined by argument filtering, the usable rules criterion, or dependency graphs, is primitive recursive in the derivational complexity induced by the direct method. This implies that the derivational complexity induced by a standard application of the dependency pair method based on traditional termination orders like KBO, LPO, and MPO is exactly the same as if those orders were applied as the only termination technique.

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Complexity, Graphs, and the Dependency Pair Method

Cited by 15 publications

References 10 publications

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

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

Automated Complexity Analysis Based on the Dependency Pair Method

The Derivational Complexity Induced by the Dependency Pair Method

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