40 research outputs found
Bisimulations Meet PCTL Equivalences for Probabilistic Automata
Probabilistic automata (PAs) have been successfully applied in formal
verification of concurrent and stochastic systems. Efficient model checking
algorithms have been studied, where the most often used logics for expressing
properties are based on probabilistic computation tree logic (PCTL) and its
extension PCTL^*. Various behavioral equivalences are proposed, as a powerful
tool for abstraction and compositional minimization for PAs. Unfortunately, the
equivalences are well-known to be sound, but not complete with respect to the
logical equivalences induced by PCTL or PCTL*. The desire of a both sound and
complete behavioral equivalence has been pointed out by Segala in 1995, but
remains open throughout the years. In this paper we introduce novel notions of
strong bisimulation relations, which characterize PCTL and PCTL* exactly. We
extend weak bisimulations that characterize PCTL and PCTL* without next
operator, respectively. Further, we also extend the framework to simulation
preorders. Thus, our paper bridges the gap between logical and behavioral
equivalences and preorders in this setting.Comment: Long version of CONCUR'11 with the same title: added extension to
simulations, countable state
Bisimulations and Logical Characterizations on Continuous-time Markov Decision Processes
In this paper we study strong and weak bisimulation equivalences for
continuous-time Markov decision processes (CTMDPs) and the logical
characterizations of these relations with respect to the continuous-time
stochastic logic (CSL). For strong bisimulation, it is well known that it is
strictly finer than CSL equivalence. In this paper we propose strong and weak
bisimulations for CTMDPs and show that for a subclass of CTMDPs, strong and
weak bisimulations are both sound and complete with respect to the equivalences
induced by CSL and the sub-logic of CSL without next operator respectively. We
then consider a standard extension of CSL, and show that it and its sub-logic
without X can be fully characterized by strong and weak bisimulations
respectively over arbitrary CTMDPs.Comment: The conference version of this paper was published at VMCAI 201
Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes
We consider PML, the probabilistic version of Hennessy-Milner logic introduced by Larsen and Skou to characterize bisimilarity over probabilistic processes without internal
nondeterminism.We provide two different interpretations for PML by considering nondeterministic and probabilistic processes as models, and we exhibit two new bisimulation-based equivalences that are in full agreement with those interpretations. Our new equivalences include
as coarsest congruences the two bisimilarities for nondeterministic and probabilistic processes proposed by Segala and Lynch. The latter equivalences are instead in agreement with two versions of Hennessy-Milner logic extended with an additional probabilistic operator
interpreted over state distributions rather than over individual states. Thus, our new interpretations of PML and the corresponding new bisimilarities offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or are mixing nondeterminism and probability in an alternating/non-alternating way
Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions
In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulation. Because these semantics may be considered too strong in the probabilistic context, Eisentraut et al. recently proposed weak distribution bisimulation. To show the flexibility of our approach based on the framework of van Glabbeek for the non-deterministic setting, we provide a novel logical characterization for the latter probabilistic equivalence as well
Revisiting Weak Simulation for Substochastic Markov Chains
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The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes
We present a spectrum of trace-based, testing, and bisimulation equivalences
for nondeterministic and probabilistic processes whose activities are all
observable. For every equivalence under study, we examine the discriminating
power of three variants stemming from three approaches that differ for the way
probabilities of events are compared when nondeterministic choices are resolved
via deterministic schedulers. We show that the first approach - which compares
two resolutions relatively to the probability distributions of all considered
events - results in a fragment of the spectrum compatible with the spectrum of
behavioral equivalences for fully probabilistic processes. In contrast, the
second approach - which compares the probabilities of the events of a
resolution with the probabilities of the same events in possibly different
resolutions - gives rise to another fragment composed of coarser equivalences
that exhibits several analogies with the spectrum of behavioral equivalences
for fully nondeterministic processes. Finally, the third approach - which only
compares the extremal probabilities of each event stemming from the different
resolutions - yields even coarser equivalences that, however, give rise to a
hierarchy similar to that stemming from the second approach.Comment: In Proceedings QAPL 2013, arXiv:1306.241