The decision problem of modal product logics with a diagonal, and faulty counter machines

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them

Model checking multi-agent systems

A multi-agent system (MAS) is usually understood as a system composed of interacting autonomous agents. In this sense, MAS have been employed successfully as a modelling paradigm in a number of scenarios, especially in Computer Science. However, the process of modelling complex and heterogeneous systems is intrinsically prone to errors: for this reason, computer scientists are typically concerned with the issue of verifying that a system actually behaves as it is supposed to, especially when a system is complex. Techniques have been developed to perform this task: testing is the most common technique, but in many circumstances a formal proof of correctness is needed. Techniques for formal verification include theorem proving and model checking. Model checking techniques, in particular, have been successfully employed in the formal verification of distributed systems, including hardware components, communication protocols, security protocols. In contrast to traditional distributed systems, formal verification techniques for MAS are still in their infancy, due to the more complex nature of agents, their autonomy, and the richer language used in the specification of properties. This thesis aims at making a contribution in the formal verification of properties of MAS via model checking. In particular, the following points are addressed: • Theoretical results about model checking methodologies for MAS, obtained by extending traditional methodologies based on Ordered Binary Decision Diagrams (OBDDS) for temporal logics to multi-modal logics for time, knowledge, correct behaviour, and strategies of agents. Complexity results for model checking these logics (and their symbolic representations). • Development of a software tool (MCMAS) that permits the specification and verification of MAS described in the formalism of interpreted systems. • Examples of application of MCMAS to various MAS scenarios (communication, anonymity, games, hardware diagnosability), including experimental results, and comparison with other tools available

Noise in Quantum and Classical Computation & Non-locality

Quantum computers seem to have capabilities which go beyond those of classical computers. A particular example which is important for cryptography is that quantum computers are able to factor numbers much faster than what seems possible on classical machines. In order to actually build quantum computers it is necessary to build sufficiently accurate hardware, which is a big challenge. In part 1 of this thesis we prove lower bounds on the accuracy of the hardware needed to do quantum computation. We also present a similar result for classical computers. One resource that quantum computers have but classical computers do not have is entanglement. In Part 2 of this thesis we study certain general aspects of entanglement in terms of quantum XOR games and non-locality

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

Software engineering: Testing real-time embedded systems using timed automata based approaches

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Real-time Embedded Systems (RTESs) have an increasing role in controlling society infrastructures that we use on a day-to-day basis. RTES behaviour is not based solely on the interactions it might have with its surrounding environment, but also on the timing requirements it induces. As a result, ensuring that an RTES behaves correctly is non-trivial, especially after adding time as a new dimension to the complexity of the testing process. This research addresses the problem of testing RTESs from Timed Automata (TA) specification by the following. First, a new Priority-based Approach (PA) for testing RTES modelled formally as UPPAAL timed automata (TA variant) is introduced. Test cases generated according to a proposed timed adequacy criterion (clock region coverage) are divided into three sets of priorities, namely boundary, out-boundary and in-boundary. The selection of which set is most appropriate for a System Under Test (SUT) can be decided by the tester according to the system type, time specified for the testing process and its budget. Second, PA is validated in comparison with four well-known timed testing approaches based on TA using Specification Mutation Analysis (SMA). To enable the validation, a set of timed and functional mutation operators based on TA is introduced. Three case studies are used to run SMA. The effectiveness of timed testing approaches are determined and contrasted according to the mutation score which shows that our PA achieves high mutation adequacy score compared with others. Third, to enhance the applicability of PA, a new testing tool (GeTeX) that deploys PA is introduced. In its current version, GeTeX supports Control Area Network (CAN) applications. GeTeX is validated by developing a prototype for that purpose. Using GeTeX, PA is also empirically validated in comparison with some TA testing approaches using a complete industrial-strength test bed. The assessment is based on fault coverage, structural coverage, the length of generated test cases and a proposed assessment factor. The assessment is based on fault coverage, structural coverage, the length of generated test cases and a proposed assessment factor. The assessment results confirmed the superiority of PA over the other test approaches. The overall assessment factor showed that structural and fault coverage scores of PA with respect to the length of its tests were better than the others proving the applicability of PA. Finally, an Analytical Hierarchy Process (AHP) decision-making framework for our PA is developed. The framework can provide testers with a systematic approach by which they can prioritise the available PA test sets that best fulfils their testing requirements. The AHP framework developed is based on the data collected heuristically from the test bed and data collected by interviewing testing experts. The framework is then validated using two testing scenarios. The decision outcomes of the AHP framework were significantly correlated to those of testing experts which demonstrated the soundness and validity of the framework.This study is funded by Damascus University, Syri

Logic and Commonsense Reasoning: Lecture Notes

MasterThese are the lecture notes of a course on logic and commonsense reasoning given to master students in philosophy of the University of Rennes 1. N.B.: Some parts of these lectures notes are sometimes largely based on or copied verbatim from publications of other authors. When this is the case, these parts are mentioned at the end of each chapter in the section “Further reading”