Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.

We prove properties of a process calculus that is designed for analyzing security protocols. Our long-term goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomial-time protocol steps, a specification method based on a compositional form of equivalence, and a logical basis for reasoning about equivalence. The process calculus is a variant of CCS, with bounded replication and probabilistic polynomial-time expressions allowed in messages and boolean tests. To avoid inconsistency between security and nondeterminism, messages are scheduled probabilistically instead of nondeterministically. We prove that evaluation of any process expression halts in probabilistic polynomial time and define a form of asymptotic protocol equivalence that allows security properties to be expressed using observational equivalence, a standard relation from programming language theory that involves quantifying over possible environments that might interact with the protocol. We develop a form of probabilistic bisimulation and use it to establish the soundness of an equational proof system based on observational equivalences. The proof system is illustrated by a formation derivation of the assertion, well-known in cryptography, that ElGamal encryption’s semantic security is equivalent to the (computational) Decision Diffie-Hellman assumption. This example demonstrates the power of probabilistic bisimulation and equational reasoning for protocol security.

The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.

This paper presents a domain model for a process algebra featuring both probabilistic and nondeterministic choice. The former is modelled using the probabilistic powerdomain of Jones and Plotkin, while the latter is modelled by a geometrically convex variant of the Plotkin powerdomain. The main result is to show that the expected laws for probability and nondeterminism are sound and complete with respect to the model. We also present an operational semantics for the process algebra, and we show that the domain model is fully abstract with respect to probabilistic bisimilarity.

We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols.

We propose decision algorithms for bisimulation relations de ned on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algorithms extend and complete other known algorithms for simpler relations and models. The algorithm we present for strong probabilistic bisimulation has polynomial time complexity, while the algorithm for weak probabilistic bisimulation is exponential; however we argue that the latter is feasible in practice.

Probability, be it inherent or explicitly introduced, has become an important issue in the verification of programs. In this paper we study a formalism which allows reasoning about programs which can act probabilistically. To describe probabilistic programs, a basic programming language with an operator for probabilistic choice is introduced and a denotational semantics is given for this language. To specify properties of probabilistic programs, standard first order logic predicates are insufficient, so a notion of probabilistic predicates is introduced. A Hoare-style proof system to check properties of probabilistic programs is given. The proof system for a sublanguage is shown to be sound and complete; the properties that can be derived are exactly the valid properties. Finally some typical examples illustrate the use of the probabilistic predicates and the proof system.

Metric-Space Denotational Semantics for Reactive Probabilistic Processes M.Z. Kwiatkowska and G.J. Norman School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Abstract We consider the calculus of Communicating Sequential Processes (CSP) [8] extended with action-guarded probabilistic choice and provide it with an operational semantics in terms of a suitable extension of Larsen and Skou's [14] reactive probabilistic transition systems. We show that a testing equivalence which identi es two processes if they pass all tests with the same probability is a congruence for a subcalculus of CSP including external and internal choice and the synchronous parallel. Using the methodology of de Bakker and Zucker [3] introduced for classical process calculi, we derive a metric-space semantic model for the calculus and show it is fully abstract.

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In this thesis we present three mathematical frameworks for the modelling of reac-tive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these systems. Two processes are identified with respect to this equivalence if, for all experiments, the probabilities of the respective processes passing a given experiment are equal. We next consider a probabilistic pro-cess calculus including external choice, internal choice, action-guarded probabilistic choice, synchronous parallel and recursion. We give operational semantics for this calculus be means of our generalised labelled transition systems and show that our equivalence is a congruence for this language. Following the methodology introduced by de Bakker & Zucker, we then give deno-tational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultra-metric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif-