Size-Change Termination, Monotonicity Constraints and Ranking Functions

Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over (abstract) variables. When only constraints of the form x>y' and x>=y' are allowed, we have size-change graphs. Both theory and practice are now more evolved in this restricted framework then in the general framework of monotonicity constraints. This paper shows that it is possible to extend and adapt some theory from the domain of size-change graphs to the general case, thus complementing previous work on monotonicity constraints. In particular, we present precise decision procedures for termination; and we provide a procedure to construct explicit global ranking functions from monotonicity constraints in singly-exponential time, which is better than what has been published so far even for size-change graphs.Comment: revised version of September 2

Polytool: polynomial interpretations as a basis for termination analysis of Logic programs

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations - very well known in the context of term rewrite systems (TRSs) - to obtain new (non-transformational) ter- mination analysis techniques for definite logic programs (LPs). This leads to an approach that can be seen as a direct generalization of the traditional techniques in termination analysis of LPs, where linear norms and level mappings are used. Our extension general- izes these to arbitrary polynomials. We extend a number of standard concepts and results on termination analysis to the context of polynomial interpretations. We also propose a constraint-based approach for automatically generating polynomial interpretations that satisfy the termination conditions. Based on this approach, we implemented a new tool, called Polytool, for automatic termination analysis of LPs

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

Stepping Stones to Inductive Synthesis of Low-Level Looping Programs

Inductive program synthesis, from input/output examples, can provide an opportunity to automatically create programs from scratch without presupposing the algorithmic form of the solution. For induction of general programs with loops (as opposed to loop-free programs, or synthesis for domain-specific languages), the state of the art is at the level of introductory programming assignments. Most problems that require algorithmic subtlety, such as fast sorting, have remained out of reach without the benefit of significant problem-specific background knowledge. A key challenge is to identify cues that are available to guide search towards correct looping programs. We present MAKESPEARE, a simple delayed-acceptance hillclimbing method that synthesizes low-level looping programs from input/output examples. During search, delayed acceptance bypasses small gains to identify significantly-improved stepping stone programs that tend to generalize and enable further progress. The method performs well on a set of established benchmarks, and succeeds on the previously unsolved "Collatz Numbers" program synthesis problem. Additional benchmarks include the problem of rapidly sorting integer arrays, in which we observe the emergence of comb sort (a Shell sort variant that is empirically fast). MAKESPEARE has also synthesized a record-setting program on one of the puzzles from the TIS-100 assembly language programming game.Comment: AAAI 201

Solving polynomial constraints for proving termination of rewriting

A termination problem can be transformed into a set of polynomial constraints. Up to now, several approaches have been studied to deal with these constraints as constraint solving problems. In this thesis, we study in depth some of these approaches, present some advances in each approach.Navarro Marset, RA. (2008). Solving polynomial constraints for proving termination of rewriting. http://hdl.handle.net/10251/13626Archivo delegad