Stochastic processes as concurrent constraint programs
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Testing preorders for probabilistic processes can be characterized by simulations
Theoretical Computer Science
Additive models of probabilistic processes
Theoretical Computer Science
Metrics for Labeled Markov Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Norm Functions for Probabilistic Bisimulations with Delays
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
Fully Abstract Characterization of Probabilistic May Testing
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Approximating Labeled Markov Processes
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Approximating labelled Markov processes
Information and Computation
Domain equations for probabilistic processes
Mathematical Structures in Computer Science
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Model checking for a probabilistic branching time logic with fairness
Distributed Computing
A randomized encoding of the π-calculus with mixed choice
Theoretical Computer Science - Process algebra
Measuring the confinement of probabilistic systems
Theoretical Computer Science - Theoretical foundations of security analysis and design II
Remarks on Testing Probabilistic Processes
Electronic Notes in Theoretical Computer Science (ENTCS)
Notes on Generative Probabilistic Bisimulation
Electronic Notes in Theoretical Computer Science (ENTCS)
A Hierarchy of Equivalences for Probabilistic Processes
FORTE '08 Proceedings of the 28th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Trace Machines for Observing Continuous-Time Markov Chains
Electronic Notes in Theoretical Computer Science (ENTCS)
Interactive Markov chains: and the quest for quantified quality
Interactive Markov chains: and the quest for quantified quality
Non-expansive ε-bisimulations for probabilistic processes
Theoretical Computer Science
Revisiting trace and testing equivalences for nondeterministic and probabilistic processes
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
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Transition systems are well-established as a semantic model for distributed systems. There are widely accepted preorders that serve as criteria for refinement of a more abstract transition system to a more concrete one. To reason about probabilistic phenomena such as failure rates, we need to extend models and methods that have proven successful for non-probabilistic systems to a probabilistic setting. In this paper, we consider a model of probabilistic transition systems, containing probabilistic choice and nondeterministic choice as independent concepts. We present a notion of testing for these systems. Our main contributions are denotational characterizations of the testing preorders. The characterizations are given in terms of chains for may-testing and refusal chains for must-testing, that are analogous to traces and failures in denotational models of CSP. Refinement corresponds to inclusion between chains and refusal chains modulo closure operations. The preorders are shown to be compositional. We also show that when restricted to non-probabilistic systems, these preorders collapse to the standard simulation and refusal- simulation.