Proving Termination of Integer Term Rewriting

Fuhs, Carsten; Giesl, Jürgen; Plücker, Martin; Schneider–Kamp, Peter; Falke, Stephan

doi:10.1007/978-3-642-02348-4_3

Cited by 35 publications

(49 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1, we regard TRSs where the integers and operations like "−", ">", " =" are built in [8] and we represent objects by terms. So essentially, for any class C with n fields we introduce an n-ary function symbol C whose arguments correspond to the fields of C. Hence, the object List(next = null) is represented by the term List(null).…”

Section: Definition 4 (Equality Refinementmentioning

confidence: 99%

“…In this way, we can benefit from the fact that rewrite techniques can automatically generate suitable well-founded orders comparing arbitrary forms of terms. Moreover, by using TRSs with built-in integers [8], our approach is not only powerful for algorithms on user-defined data structures, but also for algorithms on pre-defined data types like integers.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Termination Graphs for Java Bytecode

Brockschmidt¹,

Otto²,

Essen³

et al. 2010

Verification, Induction, Termination Analysis

Self Cite

View full text Add to dashboard Cite

Abstract. To prove termination of Java Bytecode (JBC) automatically, we transform JBC to finite termination graphs which represent all possible runs of the program. Afterwards, the graph can be translated into "simple" formalisms like term rewriting and existing tools can be used to prove termination of the resulting term rewrite system (TRS). In this paper we show that termination graphs indeed capture the semantics of JBC correctly. Hence, termination of the TRS resulting from the termination graph implies termination of the original JBC program.

show abstract

Section: Definition 4 (Equality Refinementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Termination Graphs for Java Bytecode

Brockschmidt¹,

Otto²,

Essen³

et al. 2010

Verification, Induction, Termination Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is also indicated by our experiments when comparing the implementation of our determinacy analysis in AProVE with the determinacy analysis implemented in CiaoPP [27]. 14 We again tested both tools on all 477 logic programs from the TPDB. On definite programs, CiaoPP was clearly more powerful (it proved determinacy for 132 out of 300 programs, whereas AProVE only succeeded for 19 programs).…”

Section: Theorem 28 (Soundness Of Determinacy Criterion)mentioning

confidence: 73%

“…12 However, our implementation currently does not treat built-in integer arithmetic, while [10,11,12,29] handle linear arithmetic constraints. 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 and Term Rewriting — A General Methodology for Analyzing Logic Programs

Giesl

Ströder

Schneider–Kamp

et al. 2013

Logic-Based Program Synthesis and Transformation

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…From the termination graph, one can generate a TRS with built-in integers [17] that only terminates if the original program terminates. To this end, in [25] we showed how to encode each state of a termination graph as a term and each edge as a rewrite rule.…”

Section: Proving Termination Via Term Rewritingmentioning

confidence: 99%

Automated Termination Proofs for Java Programs with Cyclic Data

Brockschmidt

Musiol

Otto

et al. 2012

Computer Aided Verification

Self Cite

View full text Add to dashboard Cite

Abstract. In earlier work, we developed a technique to prove termination of Java programs automatically: first, Java programs are automatically transformed to term rewrite systems (TRSs) and then, existing methods and tools are used to prove termination of the resulting TRSs. In this paper, we extend our technique in order to prove termination of algorithms on cyclic data such as cyclic lists or graphs automatically. We implemented our technique in the tool AProVE and performed extensive experiments to evaluate its practical applicability.

show abstract

Proving Termination of Integer Term Rewriting

Abstract: Abstract. When using rewrite techniques for termination analysis of programs, a main problem are pre-defined data types like integers. We extend term rewriting by built-in integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically.

Cited by 35 publications

References 28 publications

Termination Graphs for Java Bytecode

Termination Graphs for Java Bytecode

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

Automated Termination Proofs for Java Programs with Cyclic Data

Contact Info

Product

Resources

About