Automated Complexity Analysis Based on the Dependency Pair Method

Hirokawa, Nao; Moser, Georg

doi:10.1007/978-3-540-71070-7_32

Cited by 68 publications

(165 citation statements)

References 33 publications

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“…Different notions of complexity have been proposed for TRSs.In this paper, we focus on innermost runtime complexity [20], which corresponds to the notion of complexity used for programming languages. Here, one only considers rewrite sequences starting with basic terms f(t1, .…”

Section: From Evaluation Graphs To Trss -Complexity Analysismentioning

confidence: 99%

“…In general, for any R ′ ⊆ R, the function irc R ′ ,R maps any n ∈ N to the maximal number of i → R ′ -steps that occur in any sequence of i → R -steps starting with a basic term t where |t| ≤ n. Related notions of "relative" complexity for TRSs were used in, e.g., [4,20,31,41]. Most existing automated complexity provers can also approximate irc R ′ ,R asymptotically.…”

Section: Theorem 23 (Soundness Of Complexity Analysis I)mentioning

confidence: 99%

See 1 more Smart Citation

Symbolic Evaluation Graphs and Term Rewriting — A General Methodology for Analyzing Logic Programs

Giesl

Ströder

Schneider–Kamp

et al. 2013

Logic-Based Program Synthesis and Transformation

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There exist many powerful techniques to analyze termination and complexity of term rewrite systems (TRSs). Our goal is to use these techniques for the analysis of other programming languages as well. For instance, approaches to prove termination of definite logic programs by a transformation to TRSs have been studied for decades. However, a challenge is to handle languages with more complex evaluation strategies (such as Prolog, where predicates like the cut influence the control flow). In this paper, we present a general methodology for the analysis of such programs. Here, the logic program is first transformed into a symbolic evaluation graph which represents all possible evaluations in a finite way. Afterwards, different analyses can be performed on these graphs. In particular, one can generate TRSs from such graphs and apply existing tools for termination or complexity analysis of TRSs to infer information on the termination or complexity of the original logic program.

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Section: From Evaluation Graphs To Trss -Complexity Analysismentioning

confidence: 99%

Section: Theorem 23 (Soundness Of Complexity Analysis I)mentioning

confidence: 99%

Symbolic Evaluation Graphs and Term Rewriting — A General Methodology for Analyzing Logic Programs

Giesl

Ströder

Schneider–Kamp

et al. 2013

Logic-Based Program Synthesis and Transformation

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show abstract

“…Inspired by a comment from one of our reviewers, we examined the relationship to the field of runtime complexity, as described in [12]. The notion of the runtime complexity of a rewrite system is similar to the IR-boundedness property.…”

Section: Relationship To Runtime Complexitymentioning

confidence: 99%

On Forward Closure and the Finite Variant Property

Bouchard

Gero

Lynch

et al. 2013

Frontiers of Combining Systems

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Abstract. Equational unification is an important research area with many applications, such as cryptographic protocol analysis. Unification modulo a convergent term rewrite system is undecidable, even with just a single rule. To identify decidable (and tractable) cases, two paradigms have been developed -Basic Syntactic Mutation [14] and the Finite Variant Property [6]. Inspired by the Basic Syntactic Mutation approach, we investigate the notion of forward closure along with suitable redundancy constraints. We show that a convergent term rewriting system R has a finite forward closure if and only if R has the finite variant property. We also show the undecidability of the finiteness of forward closure, therefore determining if a system has the finite variant property is undecidable.

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

Section: Introductionmentioning

confidence: 99%

“…In this paper, we present a fresh adaptation of the DP framework for innermost runtime complexity analysis [15]. In contrast to [3,15,16], we follow the original DP framework closely.…”

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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Automated Complexity Analysis Based on the Dependency Pair Method

Cited by 68 publications

References 33 publications

Symbolic Evaluation Graphs and Term Rewriting — A General Methodology for Analyzing Logic Programs

Symbolic Evaluation Graphs and Term Rewriting — A General Methodology for Analyzing Logic Programs

On Forward Closure and the Finite Variant Property

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

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