Automated Termination Proofs for Java Programs with Cyclic Data

Brockschmidt, Marc; Musiol, Richard; Otto, Carsten; Giesl, Jürgen

doi:10.1007/978-3-642-31424-7_13

Cited by 27 publications

(45 citation statements)

References 31 publications

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“…Therefore, runtime complexity corresponds to the usual notion of "complexity" for programs [4,5]. Note that most termination techniques which transform programs to TRSs (e.g., [8,13,14,28]) result in rewrite systems where one only regards innermost rewrite sequences. This also holds for techniques to analyze termination of languages like Haskell by term rewriting [13], although Haskell has a lazy (outermost) evaluation strategy.…”

Section: Runtime Complexity Of Term Rewritingmentioning

confidence: 99%

“…Techniques for automated termination analysis of term rewriting are very powerful and have been successfully used to analyze termination of programs in many different languages (e.g., Java [8,28], Haskell [13], and Prolog [14]). Hence, by adapting these termination techniques, the ultimate goal is to obtain approaches which can also analyze the complexity of programs automatically.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Runtime Complexity Of Term Rewritingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analyzing Innermost Runtime Complexity of Term Rewriting by Dependency Pairs

Noschinski¹,

Emmes

Giesl

2013

J Autom Reasoning

Self Cite

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show abstract

“…However, decomposability is a restriction and there are programs in the TPDB whose complexity we cannot analyze, because our graph construction yields a non-decomposable evaluation graph. 9 For instance, the graph in Ex. 21 is not decomposable.…”

Section: Definition 24 (Decomposable Graphs)mentioning

confidence: 99%

“…But our approach could be extended by generating TRSs with built-in integers [14] from the evaluation graphs. This was also done in our approaches for termination analysis of Java via term rewriting [7,9].…”

Section: Theorem 27 (Soundness Of Complexity Analysis Ii)mentioning

confidence: 99%

“…Symbolic evaluation graphs also represent those aspects of the program that cannot easily be expressed in term rewriting. We also developed similar approaches for other programming languages like Java and Haskell [7,8,9,17]. For Prolog, the transformation from the program to the symbolic evaluation graph relies on a new "linear" operational semantics which we presented in [40].…”

Section: Introductionmentioning

confidence: 99%

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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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Certified Abstract Cost Analysis

Albert

Hähnle

Merayo

et al. 2021

Fundamental Approaches to Software Engineering

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A program containing placeholders for unspecified statements or expressions is called an abstract (or schematic) program. Placeholder symbols occur naturally in program transformation rules, as used in refactoring, compilation, optimization, or parallelization. We present a generalization of automated cost analysis that can handle abstract programs and, hence, can analyze the impact on the cost of program transformations. This kind of relational property requires provably precise cost bounds which are not always produced by cost analysis. Therefore, we certify by deductive verification that the inferred abstract cost bounds are correct and sufficiently precise. It is the first approach solving this problem. Both, abstract cost analysis and certification, are based on quantitative abstract execution (QAE) which in turn is a variation of abstract execution, a recently developed symbolic execution technique for abstract programs. To realize QAE the new concept of a cost invariant is introduced. QAE is implemented and runs fully automatically on a benchmark set consisting of representative optimization rules.

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Automated Termination Proofs for Java Programs with Cyclic Data

Cited by 27 publications

References 31 publications

Analyzing Innermost Runtime Complexity of Term Rewriting by Dependency Pairs

Analyzing Innermost Runtime Complexity of Term Rewriting by Dependency Pairs

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

Certified Abstract Cost Analysis

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