20,298 research outputs found

    Model checking probabilistic and stochastic extensions of the pi-calculus

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    We present an implementation of model checking for probabilistic and stochastic extensions of the pi-calculus, a process algebra which supports modelling of concurrency and mobility. Formal verification techniques for such extensions have clear applications in several domains, including mobile ad-hoc network protocols, probabilistic security protocols and biological pathways. Despite this, no implementation of automated verification exists. Building upon the pi-calculus model checker MMC, we first show an automated procedure for constructing the underlying semantic model of a probabilistic or stochastic pi-calculus process. This can then be verified using existing probabilistic model checkers such as PRISM. Secondly, we demonstrate how for processes of a specific structure a more efficient, compositional approach is applicable, which uses our extension of MMC on each parallel component of the system and then translates the results into a high-level modular description for the PRISM tool. The feasibility of our techniques is demonstrated through a number of case studies from the pi-calculus literature

    Abstract Interpretation for Probabilistic Termination of Biological Systems

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    In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. In this paper, we refine the approach in order to address probabilistic termination properties. More in details, we introduce a refinement of the abstract LTS semantics and we abstract the probabilistic semantics using a variant of Interval Markov Chains. The abstract probabilistic model safely approximates a set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination

    Probabilistic Operational Semantics for the Lambda Calculus

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    Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics are both inductively and coinductively defined. Moreover, small-step and big-step semantics are shown to produce identical outcomes, both in call-by- value and in call-by-name. Plotkin's CPS translation is extended to accommodate the choice operator and shown correct with respect to the operational semantics. Finally, the expressive power of the obtained system is studied: the calculus is shown to be sound and complete with respect to computable probability distributions.Comment: 35 page

    Verification of Linear Optical Quantum Computing using Quantum Process Calculus

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    We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and prove that they are behaviourally equivalent. We extend the theory of behavioural equivalence in the process calculus Communicating Quantum Processes (CQP) to include multiple particles (namely photons) as information carriers, described by Fock states or number states. We summarise the theory in this paper, including the crucial result that equivalence is a congruence, meaning that it is preserved by embedding in any context. In previous work, we have used quantum process calculus to model LOQC but without verifying models against specifications. In this paper, for the first time, we are able to carry out verification. We illustrate this approach by describing and verifying two models of an LOQC CNOT gate.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
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