Termination Proofs for Logic Programs with Tabling

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic programs. In particular, tabled execution of logic programs terminates more often than execution based on SLD-resolution. In this article, we introduce two notions of universal termination of logic programming with Tabling: quasi-termination and (the stronger notion of) LG-termination. We present sufficient conditions for these two notions of termination, namely quasi-acceptability and LG-acceptability, and we show that these conditions are also necessary in case the tabling is well-chosen. Starting from these conditions, we give modular termination proofs, i.e., proofs capable of combining termination proofs of separate programs to obtain termination proofs of combined programs. Finally, in the presence of mode information, we state sufficient conditions which form the basis for automatically proving termination in a constraint-based way.Comment: 48 pages, 6 figures, submitted to ACM Transactions on Computational Logic (TOCL

Non-simplifying Graph Rewriting Termination

So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly with trees. In a former paper, we showed the benefit of encoding linguistic structures by graphs and of using graph rewriting rules to compute on those structures. Justified by some linguistic considerations, graph rewriting is characterized by two features: first, there is no node creation along computations and second, there are non-local edge modifications. Under these hypotheses, we show that uniform termination is undecidable and that non-uniform termination is decidable. We describe two termination techniques based on weights and we give complexity bound on the derivation length for these rewriting system.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599

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

A generic framework for context-sensitive analysis of modular programs

Context-sensitive analysis provides information which is potentially more accurate than that provided by context-free analysis. Such information can then be applied in order to validate/debug the program and/or to specialize the program obtaining important improvements. Unfortunately, context-sensitive analysis of modular programs poses important theoretical and practical problems. One solution, used in several proposals, is to resort to context-free analysis. Other proposals do address context-sensitive analysis, but are only applicable when the description domain used satisfies rather restrictive properties. In this paper, we argüe that a general framework for context-sensitive analysis of modular programs, Le., one that allows using all the domains which have proved useful in practice in the non-modular setting, is indeed feasible and very useful. Driven by our experience in the design and implementation of analysis and specialization techniques in the context of CiaoPP, the Ciao system preprocessor, in this paper we discuss a number of design goals for context-sensitive analysis of modular programs as well as the problems which arise in trying to meet these goals. We also provide a high-level description of a framework for analysis of modular programs which does substantially meet these objectives. This framework is generic in that it can be instantiated in different ways in order to adapt to different contexts. Finally, the behavior of the different instantiations w.r.t. the design goals that motivate our work is also discussed

Specification and Construction of Control Flow Semantics

In this paper we propose a visual language CFSL for specifying control flow semantics of programming languages. We also present a translation from CFSL to graph production systems (GPS) for flow graph construction; that is, any CFSL specification, say for a language L, gives rise to a GPS that constructs from any L-program (represented as an abstract syntax graph) the corresponding flow graph. The specification language is rich enough to capture complex language constructs, including all of Java

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools have been developed over the years to address this problem. Ensuring reliability of those tools is therefore an important issue. In this paper we present a library formalizing important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools

An efficient, parametric fixpoint algorithm for analysis of java bytecode

Abstract interpretation has been widely used for the analysis of object-oriented languages and, in particular, Java source and bytecode. However, while most existing work deals with the problem of flnding expressive abstract domains that track accurately the characteristics of a particular concrete property, the underlying flxpoint algorithms have received comparatively less attention. In fact, many existing (abstract interpretation based—) flxpoint algorithms rely on relatively inefHcient techniques for solving inter-procedural caligraphs or are speciflc and tied to particular analyses. We also argüe that the design of an efficient fixpoint algorithm is pivotal to supporting the analysis of large programs. In this paper we introduce a novel algorithm for analysis of Java bytecode which includes a number of optimizations in order to reduce the number of iterations. The algorithm is parametric -in the sense that it is independent of the abstract domain used and it can be applied to different domains as "plug-ins"-, multivariant, and flow-sensitive. Also, is based on a program transformation, prior to the analysis, that results in a highly uniform representation of all the features in the language and therefore simplifies analysis. Detailed descriptions of decompilation solutions are given and discussed with an example. We also provide some performance data from a preliminary implementation of the analysis

Unification modulo a partial theory of exponentiation

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.Comment: In Proceedings UNIF 2010, arXiv:1012.455