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

Expressiveness of the modal mu-calculus on monotone neighborhood structures

We characterize the expressive power of the modal mu-calculus on monotone neighborhood structures, in the style of the Janin-Walukiewicz theorem for the standard modal mu-calculus. For this purpose we consider a monadic second-order logic for monotone neighborhood structures. Our main result shows that the monotone modal mu-calculus corresponds exactly to the fragment of this second-order language that is invariant for neighborhood bisimulations

The Glory of the Past and Geometrical Concurrency

This paper contributes to the general understanding of the geometrical model of concurrency that was named higher dimensional automata (HDAs) by Pratt. In particular we investigate modal logics for such models and their expressive power in terms of the bisimulation that can be captured. The geometric model of concurrency is interesting from two main reasons: its generality and expressiveness, and the natural way in which autoconcurrency and action refinement are captured. Logics for this model, though, are not well investigated, where a simple, yet adequate, modal logic over HDAs was only recently introduced. As this modal logic, with two existential modalities, during and after, captures only split bisimulation, which is rather low in the spectrum of van Glabbeek and Vaandrager, the immediate question was what small extension of this logic could capture the more fine-grained hereditary history preserving bisimulation (hh)? In response, the work in this paper provides several insights. One is the fact that the geometrical aspect of HDAs makes it possible to use for capturing the hh-bisimulation, a standard modal logic that does not employ event variables, opposed to the two logics (over less expressive models) that we compare with. The logic that we investigate here uses standard past modalities and extends the previously introduced logic (called HDML) that had only forward, action-labelled, modalities. Besides, we try to understand better the above issues by introducing a related model that we call ST-configuration structures, which extend the configuration structures of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and prove the earlier results in the light of this new model. These offer a different view on why the past modalities and geometrical concurrency capture the hereditary history preserving bisimulation. Additional correlating insights are also gained.Comment: 17 pages, 7 figure

Bisimulations on data graphs

Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called “data graphs”), and where observers can test for equality or inequality of data values (e.g., asking the attribute ‘name’ of a node to be different from that of all its neighbors). The present work constitutes a first investigation of “data aware” bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath —a language that extends modal logics like PDL with tests for data equality— with and without transitive closure operators. We show that in general the problem is PSPACE-complete, but identify several restrictions that yield better complexity bounds (CO- NP, PTIME) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.Fil: Abriola, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Barceló, Pablo. Universidad de Chile; ChileFil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentin

Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs

Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDPs while preserving PCTL properties it satisfies. We discuss different interpretations of uncertainty in the models which are studied in the literature and that result in two different definitions of bisimulations. We give algorithms to compute the quotients of these bisimulations in time polynomial in the size of the model and exponential in the uncertain branching. Finally, we show by a case study that large models in practice can have small branching and that a substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784

A Logic with Reverse Modalities for History-preserving Bisimulations

We introduce event identifier logic (EIL) which extends Hennessy-Milner logic by the addition of (1) reverse as well as forward modalities, and (2) identifiers to keep track of events. We show that this logic corresponds to hereditary history-preserving (HH) bisimulation equivalence within a particular true-concurrency model, namely stable configuration structures. We furthermore show how natural sublogics of EIL correspond to coarser equivalences. In particular we provide logical characterisations of weak history-preserving (WH) and history-preserving (H) bisimulation. Logics corresponding to HH and H bisimulation have been given previously, but not to WH bisimulation (when autoconcurrency is allowed), as far as we are aware. We also present characteristic formulas which characterise individual structures with respect to history-preserving equivalences.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations

We argue that European transport regulations can be formalized within the Sigma^1_1 fragment of monadic second order logic, and possibly weaker fragments including linear temporal logic. We consider several articles in the regulation to verify these claims