Results 1  10
of
23
Probabilistic Simulations for Probabilistic Processes
, 1994
"... 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 ..."
Abstract

Cited by 367 (22 self)
 Add to MetaCart
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.
Priorities in process algebra
, 1999
"... This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized ..."
Abstract

Cited by 120 (12 self)
 Add to MetaCart
(Show Context)
This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized choice, orrealtime behavior. Approaches to priority in process algebras can be classi ed according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global preemption and static priorities and led to formalisms for modeling interrupts and aspects of realtime, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of preemption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the e cient encoding of realtime semantics. Technically, this chapter studies the di erent models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local preemption. In each case the operational semantics of CCS is modi ed appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for di erent processalgebraic settings are discussed.
Metrics for Labelled Markov Systems
, 2001
"... 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 ..."
Abstract

Cited by 50 (10 self)
 Add to MetaCart
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.
A probabilistic polynomialtime calculus for analysis of cryptographic protocols
 Electronic Notes in Theoretical Computer Science
, 2001
"... We prove properties of a process calculus that is designed for analyzing security protocols. Our longterm goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomialtime protocol steps, a spec ..."
Abstract

Cited by 48 (8 self)
 Add to MetaCart
We prove properties of a process calculus that is designed for analyzing security protocols. Our longterm goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomialtime 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 polynomialtime 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, wellknown in cryptography, that ElGamal encryption’s semantic security is equivalent to the (computational) Decision DiffieHellman assumption. This example demonstrates the power of probabilistic bisimulation and equational reasoning for protocol security.
Decision Algorithms for Probabilistic Bisimulation
, 2002
"... 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 algori ..."
Abstract

Cited by 33 (3 self)
 Add to MetaCart
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.
Axioms for Probability and Nondeterminism
 ENTCS
, 2003
"... 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 resu ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
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.
Randomized Selfstabilizing and Space Optimal Leader Election under Arbitrary Scheduler on Rings
, 1999
"... We present a randomized selfstabilizing leader election protocol and a randomized selfstabilizing 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 protocol ..."
Abstract

Cited by 30 (10 self)
 Add to MetaCart
We present a randomized selfstabilizing leader election protocol and a randomized selfstabilizing 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.
Verifying Probabilistic Programs Using A Hoare Like Logic
, 2002
"... 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 oper ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
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 Hoarestyle 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 semantics for reactive probabilistic processes
, 1997
"... In this thesis we present three mathematical frameworks for the modelling of reactive 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 syst ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
In this thesis we present three mathematical frameworks for the modelling of reactive 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 process calculus including external choice, internal choice, actionguarded 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 denotational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultrametric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif