832 research outputs found
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
On Bisimulations for Description Logics
We study bisimulations for useful description logics. The simplest among the
considered logics is (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of we have any sublogic
of that extends . We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.Comment: 42 page
Bisimulation theory for switching linear systems
A general notion of hybrid bisimulation is proposed and related to the notions of algebraic, state-space and input-output equivalences for the class of switching linear systems. An algebraic characterization of hybrid bisimulations and a procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Bisimulation-based reduction and simulation-based abstraction are defined and characterized. Connections with observability are investigated
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
Equivalence of switching linear systems by bisimulation
A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and inputâoutput equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud
\u
A coalgebraic semantics for causality in Petri nets
In this paper we revisit some pioneering efforts to equip Petri nets with
compact operational models for expressing causality. The models we propose have
a bisimilarity relation and a minimal representative for each equivalence
class, and they can be fully explained as coalgebras on a presheaf category on
an index category of partial orders. First, we provide a set-theoretic model in
the form of a a causal case graph, that is a labeled transition system where
states and transitions represent markings and firings of the net, respectively,
and are equipped with causal information. Most importantly, each state has a
poset representing causal dependencies among past events. Our first result
shows the correspondence with behavior structure semantics as proposed by
Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and
have infinitely many states, but we show how they can be refined to get an
equivalent finitely-branching model. In it, states are equipped with
symmetries, which are essential for the existence of a minimal, often
finite-state, model. The next step is constructing a coalgebraic model. We
exploit the fact that events can be represented as names, and event generation
as name generation. Thus we can apply the Fiore-Turi framework: we model causal
relations as a suitable category of posets with action labels, and generation
of new events with causal dependencies as an endofunctor on this category. Then
we define a well-behaved category of coalgebras. Our coalgebraic model is still
infinite-state, but we exploit the equivalence between coalgebras over a class
of presheaves and History Dependent automata to derive a compact
representation, which is equivalent to our set-theoretical compact model.
Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin
Ackermann Encoding, Bisimulations, and OBDDs
We propose an alternative way to represent graphs via OBDDs based on the
observation that a partition of the graph nodes allows sharing among the
employed OBDDs. In the second part of the paper we present a method to compute
at the same time the quotient w.r.t. the maximum bisimulation and the OBDD
representation of a given graph. The proposed computation is based on an
OBDD-rewriting of the notion of Ackermann encoding of hereditarily finite sets
into natural numbers.Comment: To appear on 'Theory and Practice of Logic Programming
Sigref â A Symbolic Bisimulation Tool Box
We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation.
We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center âAutomatic Verification and Analysis of Complex Systemsâ (SFB/TR 14 AVACS). See www.avacs.org for more information
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 âdata graphsâ), and where observers can test for equality or inequality of data values (e.g., asking the attribute ânameâ of a node to be different from that of all its neighbors). The present work constitutes a first investigation of âdata awareâ bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath âa language that extends modal logics like PDL with tests for data equalityâ 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 CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de InvestigaciĂłn En Ciencias de la ComputaciĂłn. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de InvestigaciĂłn En Ciencias de la Computacion; ArgentinaFil: BarcelĂł, Pablo. Universidad de Chile; ChileFil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de InvestigaciĂłn En Ciencias de la ComputaciĂłn. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de InvestigaciĂłn En Ciencias de la Computacion; Argentin
- âŠ