Non-termination analysis of logic programs with integer arithmetics

Voets, Dean; Schreye, Danny De

doi:10.1017/s1471068411000159

Cited by 10 publications

(9 citation statements)

References 13 publications

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“…A significant body of work has been done on termination of logic programs under top-down evaluation (De Schreye and Decorte 1994;Voets and De Schreye 2011;Marchiori 1996;Ohlebusch 2001;Codish et al 2005;Serebrenik and De Schreye 2005;Nishida and Vidal 2010;Schneider-Kamp et al 2009;Schneider-Kamp et al 2010;Nguyen et al 2007;Bruynooghe et al 2007;Bonatti 2004;Baselice et al 2009) and in the area of term rewriting (Zantema 1995;Sternagel and Middeldorp 2008;Arts and Giesl 2000;Endrullis et al 2008;Ferreira and Zantema 1996). Termination properties of query evaluation for normal programs under tabling have been studied in (Riguzzi and Swift 2013;Riguzzi and Swift 2014;Verbaeten et al 2001).…”

Section: Related Workmentioning

confidence: 99%

Using linear constraints for logic program termination analysis

Greco¹,

Molinaro²,

Trubitsyna³

2016

Theory and Practice of Logic Programming

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It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their introduction is that the evaluation of a program might not terminate and checking whether it terminates or not is undecidable. To cope with this problem, several classes of logic programs have been proposed where the use of function symbols is restricted but the program evaluation termination is guaranteed. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel classes of rule-bounded and cycle-bounded programs, which overcome different limitations of current approaches by performing a more global analysis of how terms are propagated from the body to the head of rules. Results on the correctness, the complexity, and the expressivity of the proposed approach are provided. Under consideration in Theory and Practice of Logic Programming (TPLP).

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Section: Related Workmentioning

confidence: 99%

Using linear constraints for logic program termination analysis

Greco¹,

Molinaro²,

Trubitsyna³

2016

Theory and Practice of Logic Programming

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“…Despite their differences, the functionality of the two systems overlaps when computing queries to stratified programs, or grounding non-stratified programs. Repeated independent comparisons of DLV, XSB and other systems have been made in and 2011by [OpenRuleBench 2011. Although the last such comparison was performed in March 2011, the comparisons as a whole illustrate general performance differences between the two systems.…”

Section: Performance Overheadmentioning

confidence: 99%

“…The majority of work has focussed on analyzing termination of definite programs under SLD resolution and its extensions, such as arithmetic (e.g., [Decorte et al 1999;Voets and De Schreye 2011]). Another recent branch of work has focused on defining classes of disjunctive programs for which a model-preserving ground instantiation can be obtained in finite time, along with algorithms to produce these instantiations [Baselice et al 2009;Calimeri et al 2008].…”

Section: Introductionmentioning

confidence: 99%

Terminating Evaluation of Logic Programs with Finite Three-Valued Models

Riguzzi

Swift

2014

ACM Trans. Comput. Logic

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As evaluation methods for logic programs have become more sophisticated, the classes of programs for which termination can be guaranteed have expanded. From the perspective of answer set programs that include function symbols, recent work has identified classes for which grounding routines can terminate either on the entire program [Calimeri et al. 2008] or on suitable queries [Baselice et al. 2009]. From the perspective of tabling, it has long been known that a tabling technique called subgoal abstraction provides good termination properties for definite programs [Tamaki and Sato 1986], and this result was recently extended to stratified programs via the class of bounded term-size programs [Riguzzi and Swift 2013]. However, rather than asking what class of programs terminate for a given evaluation method, it is natural to start with a class of programs that have finite models, and then determine whether given evaluation methods terminate for that class. In this paper we define the class of strongly bounded term-size programs and show both that this class is equivalent to programs with finite well-founded models, and that for normal programs it strictly includes the finitely ground programs of [Calimeri et al. 2008]. We then show that tabling extended with suitable forms of subgoal abstraction terminates on all queries to such programs with an asymptotic complexity equal to the best known. Furthermore, tabling with subgoal abstraction produces a residual program that can be sent to an answer set programming system. Finally, we describe the implementation of subgoal abstraction within the SLG-WAM of XSB and provide performance results.

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“…A significant body of work has been done on termination of logic programs under top-down evaluation [9,36,22,25,8,30,24,28,29,23,5,4,3] and in the area of term rewriting [37,32,2,11,12]. Termination properties of query evaluation for normal programs under tabling have been studied in [26,27,34].…”

Section: Related Workmentioning

confidence: 99%

Checking Termination of Logic Programs with Function Symbols through Linear Constraints

Greco

Molinaro

Trubitsyna

2014

Rules on the Web. From Theory to Applications

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Abstract. Enriching answer set programming with function symbols makes modeling easier, increases the expressive power, and allows us to deal with infinite domains. However, this comes at a cost: common inference tasks become undecidable. To cope with this issue, recent research has focused on finding trade-offs between expressivity and decidability by identifying classes of logic programs that impose limitations on the use of function symbols but guarantee decidability of common inference tasks. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel class of rulebounded programs. While current techniques perform a limited analysis of how terms are propagated from an individual argument to another, our technique is able to perform a more global analysis, thereby overcoming several limitations of current approaches. We also present a further class of cycle-bounded programs where groups of rules are analyzed together. We show different results on the correctness and the expressivity of the proposed techniques.

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Non-termination analysis of logic programs with integer arithmetics

Cited by 10 publications

References 13 publications

Using linear constraints for logic program termination analysis

Using linear constraints for logic program termination analysis

Terminating Evaluation of Logic Programs with Finite Three-Valued Models

Checking Termination of Logic Programs with Function Symbols through Linear Constraints

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