A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc

SOS rule formats for convex and abstract probabilistic bisimulations

Probabilistic transition system specifications (PTSSs) in the $nt \mu f\theta / nt\mu x\theta$ format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that bisimilarity is a congruence for all operator defined in such format. Starting from the $nt \mu f\theta / nt\mu x\theta$ format, we obtain restricted formats that guarantee that three coarser bisimulation equivalences are congruences. We focus on (i) Segala's variant of bisimulation that considers combined transitions, which we call here "convex bisimulation"; (ii) the bisimulation equivalence resulting from considering Park & Milner's bisimulation on the usual stripped probabilistic transition system (translated into a labelled transition system), which we call here "probability obliterated bisimulation"; and (iii) a "probability abstracted bisimulation", which, like bisimulation, preserves the structure of the distributions but instead, it ignores the probability values. In addition, we compare these bisimulation equivalences and provide a logic characterization for each of them.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634

Smart Sampling for Lightweight Verification of Markov Decision Processes

Markov decision processes (MDP) are useful to model optimisation problems in concurrent systems. To verify MDPs with efficient Monte Carlo techniques requires that their nondeterminism be resolved by a scheduler. Recent work has introduced the elements of lightweight techniques to sample directly from scheduler space, but finding optimal schedulers by simple sampling may be inefficient. Here we describe "smart" sampling algorithms that can make substantial improvements in performance.Comment: IEEE conference style, 11 pages, 5 algorithms, 11 figures, 1 tabl

Describing secure interfaces with interface automata

Interface automata are a model that allows for the representation of stateful interfaces. In this paper we introduce a variant of interface automata, which we call interface structure for security (ISS), that allows for the modelling of security. We focus on the property of non interference, more precisely in bisimulation-based non interference for reactive systems. We define the notion of compatible interfaces in this setting meaning that they can be composed so that a secure interface can be synthesized from the composition. In fact, we provide an algorithm that determines whether an ISS can be made secure by controlling (more specifically, pruning) some public input actions, and if so, synthesize the secure ISS. In addition, we also provide some sufficient conditions on the components ISS to ensure that their composition is secure (and hence no synthesis process is needed).Fil: Lee, Matias David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

Bisimulations for non-deterministic labelled Markov processes

We extend the theory of labelled Markov processes to include internal non-determinism, which is a fundamental concept for the further development of a process theory with abstraction on non-deterministic continuous probabilistic systems. We define non-deterministic labelled Markov processes (NLMP) and provide three definitions of bisimulations: a bisimulation following a traditional characterisation; a state-based bisimulation tailored to our 'measurable' non-determinism; and an event-based bisimulation. We show the relations between them, including the fact that the largest state bisimulation is also an event bisimulation. We also introduce a variation of the Hennessy-Milner logic that characterises event bisimulation and is sound with respect to the other bisimulations for an arbitrary NLMP. This logic, however, is infinitary as it contains a denumerable. We then introduce a finitary sublogic that characterises all bisimulations for an image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all the notions of bisimulation we consider turn out to be equal. Finally, we show that all these bisimulation notions are different in the general case. The counterexamples that separate them turn out to be non-probabilistic NLMPs.Fil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Sanchez Terraf, Pedro Octavio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Wolovick, Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin