# Logical Characterizations of Bisimulations for Discrete Probabilistic Systems

@inproceedings{Parma2007LogicalCO, title={Logical Characterizations of Bisimulations for Discrete Probabilistic Systems}, author={Augusto Parma and Roberto Segala}, booktitle={FoSSaCS}, year={2007} }

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 satisfactionâ€¦Â

## 70 Citations

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

- Computer ScienceMFCS
- 2016

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

- Computer ScienceFormal 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.

### Algorithmic and logical characterizations of bisimulations for non-deterministic fuzzy transition systems

- Computer ScienceFuzzy Sets Syst.
- 2018

### Logical characterizations of simulation and bisimulation for fuzzy transition systems

- Computer ScienceFuzzy Sets Syst.
- 2016

### Computing Distances between Probabilistic Automata

- Computer ScienceQAPL
- 2011

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

- Computer ScienceActa Informatica
- 2014

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

- Computer ScienceACM Trans. Comput. Log.
- 2014

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

- Computer ScienceCONCUR
- 2011

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

- MathematicsArXiv
- 2011

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

- Computer Science2009 Sixth International Conference on the Quantitative Evaluation of Systems
- 2009

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.

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