9,784 research outputs found

    An Algorithm for Approximating the Satisfiability Problem of High-level Conditions

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    AbstractThe satisfiability problem is the fundamental problem in proving the conflict-freeness of specifications, or in finding a counterexample for an invalid statement. In this paper, we present a non-deterministic, monotone algorithm for this undecidable problem on graphical conditions that is both correct and complete, but in general not guaranteed to terminate. For a fragment of high-level conditions, the algorithm terminates, hence it is able to decide. Instead of enumerating all possible objects of a category to approach the problem, the algorithm uses the input condition in a constructive way to progress towards a solution. To this aim, programs over transformation rules with external interfaces are considered. We use the framework of weak adhesive HLR categories. Consequently, the algorithm is applicable to a number of replacement capable structures, such as Petri-Nets, graphs or hypergraphs

    Satisfiability Games for Branching-Time Logics

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    The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly exponential time, CTL is complete for single exponential time. Some decision procedures for these logics are known; they use tree automata, tableaux or axiom systems. In this paper we present a uniform game-theoretic framework for the satisfiability problem of these branching-time temporal logics. We define satisfiability games for the full branching-time temporal logic CTL* using a high-level definition of winning condition that captures the essence of well-foundedness of least fixpoint unfoldings. These winning conditions form formal languages of \omega-words. We analyse which kinds of deterministic {\omega}-automata are needed in which case in order to recognise these languages. We then obtain a reduction to the problem of solving parity or B\"uchi games. The worst-case complexity of the obtained algorithms matches the known lower bounds for these logics. This approach provides a uniform, yet complexity-theoretically optimal treatment of satisfiability for branching-time temporal logics. It separates the use of temporal logic machinery from the use of automata thus preserving a syntactical relationship between the input formula and the object that represents satisfiability, i.e. a winning strategy in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner closure of the input formula only. Last but not least, the games presented here come with an attempt at providing tool support for the satisfiability problem of complex branching-time logics like CTL* and CTL+

    Two-variable Logic with Counting and a Linear Order

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    We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbols). In the case of one linear order it is NEXPTIME-complete, even in the presence of the successor relation. Surprisingly, the complexity of the problem explodes when we add one binary symbol more: C2 with one linear order and in the presence of other binary predicate symbols is equivalent, under elementary reductions, to the emptiness problem for multicounter automata

    Verifying the Interplay of Authorization Policies and Workflow in Service-Oriented Architectures (Full version)

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    A widespread design approach in distributed applications based on the service-oriented paradigm, such as web-services, consists of clearly separating the enforcement of authorization policies and the workflow of the applications, so that the interplay between the policy level and the workflow level is abstracted away. While such an approach is attractive because it is quite simple and permits one to reason about crucial properties of the policies under consideration, it does not provide the right level of abstraction to specify and reason about the way the workflow may interfere with the policies, and vice versa. For example, the creation of a certificate as a side effect of a workflow operation may enable a policy rule to fire and grant access to a certain resource; without executing the operation, the policy rule should remain inactive. Similarly, policy queries may be used as guards for workflow transitions. In this paper, we present a two-level formal verification framework to overcome these problems and formally reason about the interplay of authorization policies and workflow in service-oriented architectures. This allows us to define and investigate some verification problems for SO applications and give sufficient conditions for their decidability.Comment: 16 pages, 4 figures, full version of paper at Symposium on Secure Computing (SecureCom09

    Goal-conflict detection based on temporal satisfiability checking

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    Goal-oriented requirements engineering approaches propose capturing how a system should behave through the speci ca- tion of high-level goals, from which requirements can then be systematically derived. Goals may however admit subtle situations that make them diverge, i.e., not be satis able as a whole under speci c circumstances feasible within the domain, called boundary conditions . While previous work al- lows one to identify boundary conditions for con icting goals written in LTL, it does so through a pattern-based approach, that supports a limited set of patterns, and only produces pre-determined formulations of boundary conditions. We present a novel automated approach to compute bound- ary conditions for general classes of con icting goals expressed in LTL, using a tableaux-based LTL satis ability procedure. A tableau for an LTL formula is a nite representation of all its satisfying models, which we process to produce boundary conditions that violate the formula, indicating divergence situations. We show that our technique can automatically produce boundary conditions that are more general than those obtainable through existing previous pattern-based approaches, and can also generate boundary conditions for goals that are not captured by these patterns
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