Logical Characterizations of Bisimulations for Discrete Probabilistic Systems

  title={Logical Characterizations of Bisimulations for Discrete Probabilistic Systems},
  author={Augusto Parma and Roberto Segala},
We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three Hennessy-Milner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only in the kind of diamond operator used. Compared to the Larsen and Skou logic for reactive systems, these logics introduce a new operator that measures the probability of the set of states that satisfy a formula. Moreover, the satisfaction… 

Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions

This paper studies transition relations over probability distributions in a setting with internal actions and provides new logics that characterize probabilistic strong, weak and branching bisimulation, including a novel logical characterization for the latter probabilism equivalence.

Exploring probabilistic bisimulations, part I

  • M. Hennessy
  • Computer Science
    Formal Aspects of Computing
  • 2012
It is suggested that it is natural to interpret such processes as distributions over states in a probabilistic labelled transition system, a pLTS, and it is proved that a novel form of bisimulation equivalence between distributions are both sound and complete with respect to this contextual equivalence.

Logical characterizations of simulation and bisimulation for fuzzy transition systems

Computing Distances between Probabilistic Automata

A natural modification of this distance is introduced, to obtain a discounted distance, which weakens the influence of long term transitions and compares the notions of distance to others previously defined, and proves that the distance is not expansive with respect to process algebra operators.

Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes

The new interpretations of PML and the corresponding new bisimilarities are the first ones to offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or that mix nondeterminism and probability in an alternating/nonalternating way.

Logical Characterizations of Behavioral Relations on Transition Systems of Probability Distributions

It is shown that the well-known spectrum of behavioral relations on nonprobabilistic LTSs as well as their corresponding logical characterizations in terms of Hennessy-Milner logic scales to the probabilistic setting when considering dLTSs.

Bisimulations Meet PCTL Equivalences for Probabilistic Automata

Novel notions of strong bisimulation relations are introduced, which characterizes PCTL and P CTL* exactly and are extended to extend weak bisimulations characterizing PCT l and PCTl* without next operator, respectively.

Logical, Metric, and Algorithmic Characterisations of Probabilistic Bisimulation

The Hennessy-Milner logic and the modal mu-calculus are extended with a new modality, resulting in an adequate and an expressive logic for probabilistic bisimilarity, respectively, and the correspondence of the lifting operation and the Kantorovich metric leads to a natural characterisation of bisimulations as pseudometrics which are post-fixed points of a monotone function.

Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization

A finitary sublogic is introduced that characterize both state and event bisimulation for image finite NLMP whose underlying measure space is also analytic and, in this setting, all notions ofbisimulation turn out to be equal.



A logical characterization of bisimulation for labeled Markov processes

An algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation, a logical characterization of probabilistic bisimulations for Markov processes.

Weak bisimulation is sound and complete for pCTL*

Weak Bisimulation for Probabilistic Systems

It is shown that in order to compute weak bisimulation it is sufficient to restrict attention to only a finite number of these computations, and an algorithm is presented which has polynomial-time complexity in the number of states of the transition system.

Validation of Stochastic Systems

An overview of existing types of probabilistic systems and the relationship between these models is provided, and the existence of mappings between the corresponding system types that preserve and reflect bisimilarity is explained.

Probabilistic Automata: System Types, Parallel Composition and Comparison

An overview of existing types of probabilistic systems and the relationship between these models is provided, and the existence of mappings between the corresponding system types that preserve and reflect bisimilarity is explained.

Comparative analysis of bisimulation relations on alternating and non-alternating probabilistic models

  • R. SegalaAndrea Turrini
  • Computer Science
    Second International Conference on the Quantitative Evaluation of Systems (QEST'05)
  • 2005
A taxonomy of bisimulation relations is identified that captures the existing definitions for each one of the three models, and the relations within each model and across models are compared.

Bisimulation through Probabilistic Testing

Decision Algorithms for Probabilistic Bisimulation

The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers based on probabilistic automata, a model for concurrent nondeterministic systems with randomization.

Specification and refinement of probabilistic processes

  • B. JonssonK. Larsen
  • Computer Science
    [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
  • 1991
A formalism for specifying probabilistic transition systems, which constitute a basic semantic model for description and analysis of reliability aspects of concurrent and distributed systems, is presented and it is shown that it is analogous to the extension from processes to modal transition systems.

A Hierarchy of Polynomial-Time Computable Simulations for Automata

We define and provide algorithms for computing a natural hierarchy of simulation relations on the state-spaces of ordinary transition systems, finite automata, and Buchi automata.T hese simulations