1,188 research outputs found
Expected-Delay-Summing Weak Bisimilarity for Markov Automata
A new weak bisimulation semantics is defined for Markov automata that, in
addition to abstracting from internal actions, sums up the expected values of
consecutive exponentially distributed delays possibly intertwined with internal
actions. The resulting equivalence is shown to be a congruence with respect to
parallel composition for Markov automata. Moreover, it turns out to be
comparable with weak bisimilarity for timed labeled transition systems, thus
constituting a step towards reconciling the semantics for stochastic time and
deterministic time.Comment: In Proceedings QAPL 2015, arXiv:1509.0816
Weak MSO: Automata and Expressiveness Modulo Bisimilarity
We prove that the bisimulation-invariant fragment of weak monadic
second-order logic (WMSO) is equivalent to the fragment of the modal
-calculus where the application of the least fixpoint operator is restricted to formulas that are continuous in . Our
proof is automata-theoretic in nature; in particular, we introduce a class of
automata characterizing the expressive power of WMSO over tree models of
arbitrary branching degree. The transition map of these automata is defined in
terms of a logic that is the extension of first-order
logic with a generalized quantifier , where means that there are infinitely many objects satisfying . An
important part of our work consists of a model-theoretic analysis of
.Comment: Technical Report, 57 page
On Modal {\mu}-Calculus over Finite Graphs with Bounded Strongly Connected Components
For every positive integer k we consider the class SCCk of all finite graphs
whose strongly connected components have size at most k. We show that for every
k, the Modal mu-Calculus fixpoint hierarchy on SCCk collapses to the level
Delta2, but not to Comp(Sigma1,Pi1) (compositions of formulas of level Sigma1
and Pi1). This contrasts with the class of all graphs, where
Delta2=Comp(Sigma1,Pi1)
Conflict-preserving abstraction of discrete event systems using annotated automata
This paper proposes to enhance compositional verification of the nonblocking property of discrete event systems by introducing annotated automata. Annotations store nondeterministic branching information, which would otherwise be stored in extra states and transitions. This succinct representation makes it easier to simplify automata and enables new efficientmeans of abstraction, reducing the size of automata to be composed and thus the size of the synchronous product state space encountered in verification. The abstractions proposed are of polynomial complexity, and they have been successfully applied to model check the nonblocking property of the same set of large-scale industrial examples as used in related work
Cost Preserving Bisimulations for Probabilistic Automata
Probabilistic automata constitute a versatile and elegant model for
concurrent probabilistic systems. They are equipped with a compositional theory
supporting abstraction, enabled by weak probabilistic bisimulation serving as
the reference notion for summarising the effect of abstraction. This paper
considers probabilistic automata augmented with costs. It extends the notions
of weak transitions in probabilistic automata in such a way that the costs
incurred along a weak transition are captured. This gives rise to
cost-preserving and cost-bounding variations of weak probabilistic
bisimilarity, for which we establish compositionality properties with respect
to parallel composition. Furthermore, polynomial-time decision algorithms are
proposed, that can be effectively used to compute reward-bounding abstractions
of Markov decision processes in a compositional manner
Behavioural hybrid process calculus
Process algebra is a theoretical framework for the modelling and analysis of the behaviour of concurrent discrete event systems that has been developed within computer science in past quarter century. It has generated a deeper nderstanding of the nature of concepts such as observable behaviour in the presence of nondeterminism, system composition by interconnection of concurrent component systems, and notions of behavioural equivalence of such systems. It has contributed fundamental concepts such as bisimulation, and has been successfully used in a wide range of problems and practical applications in concurrent systems. We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems. In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems. It provides a natural framework for the concurrent composition of such systems, and can deal with nondeterministic behaviour that may arise from the occurrence of internal switching events. Standard process algebraic techniques lead to the characterisation of the observable behaviour of such systems as equivalence classes under some suitably adapted notion of bisimulation
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