Using Graph Transformations and Graph Abstractions for Software Verification

In this paper we describe our intended approach for the verification of software written in imperative programming languages. We base our approach on model checking of graph transition systems, where each state is a graph and the transitions are specified by graph transformation rules. We believe that graph transformation is a very suitable technique to model the execution semantics of languages with dynamic memory allocation. Furthermore, such representation allows us to investigate the use of graph abstractions, which can mitigate the combinatorial explosion inherent to model checking. In addition to presenting our planned approach, we reason about its feasibility, and, by providing a brief comparison to other existing methods, we highlight the benefits and drawbacks that are expected

An integration of partial evaluation in a generic abstract interpretation framework

Information generated by abstract interpreters has long been used to perform program specialization. Additionally, if the abstract interpreter generates a multivariant analysis, it is also possible to perform múltiple specialization. Information about valúes of variables is propagated by simulating program execution and performing fixpoint computations for recursive calis. In contrast, traditional partial evaluators (mainly) use unfolding for both propagating valúes of variables and transforming the program. It is known that abstract interpretation is a better technique for propagating success valúes than unfolding. However, the program transformations induced by unfolding may lead to important optimizations which are not directly achievable in the existing frameworks for múltiple specialization based on abstract interpretation. The aim of this work is to devise a specialization framework which integrates the better information propagation of abstract interpretation with the powerful program transformations performed by partial evaluation, and which can be implemented via small modifications to existing generic abstract interpreters. With this aim, we will relate top-down abstract interpretation with traditional concepts in partial evaluation and sketch how the sophisticated techniques developed for controlling partial evaluation can be adapted to the proposed specialization framework. We conclude that there can be both practical and conceptual advantages in the proposed integration of partial evaluation and abstract interpretation

Verifying Monadic Second-Order Properties of Graph Programs

The core challenge in a Hoare- or Dijkstra-style proof system for graph programs is in defining a weakest liberal precondition construction with respect to a rule and a postcondition. Previous work addressing this has focused on assertion languages for first-order properties, which are unable to express important global properties of graphs such as acyclicity, connectedness, or existence of paths. In this paper, we extend the nested graph conditions of Habel, Pennemann, and Rensink to make them equivalently expressive to monadic second-order logic on graphs. We present a weakest liberal precondition construction for these assertions, and demonstrate its use in verifying non-local correctness specifications of graph programs in the sense of Habel et al.Comment: Extended version of a paper to appear at ICGT 201

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties

Resource-Bound Quantification for Graph Transformation

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems

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

Experiments with a Convex Polyhedral Analysis Tool for Logic Programs

Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We present a tool for constructing polyhedral analyses of (constraint) logic programs. The aim of the tool is to make available, with a convenient interface, state-of-the-art techniques for polyhedral analysis such as delayed widening, narrowing, "widening up-to", and enhanced automatic selection of widening points. The tool is accessible on the web, permits user programs to be uploaded and analysed, and is integrated with related program transformations such as size abstractions and query-answer transformation. We then report some experiments using the tool, showing how it can be conveniently used to analyse transition systems arising from models of embedded systems, and an emulator for a PIC microcontroller which is used for example in wearable computing systems. We discuss issues including scalability, tradeoffs of precision and computation time, and other program transformations that can enhance the results of analysis.Comment: Paper presented at the 17th Workshop on Logic-based Methods in Programming Environments (WLPE2007