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Reactive, Generative and Stratified Models of Probabilistic Processes
 Information and Computation
, 1990
"... ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ..."
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Cited by 155 (6 self)
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ion Let E; E 0 be PCCS expressions. The intermodel abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...
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 ..."
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Cited by 102 (11 self)
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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.
A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time
 Theoretical Computer Science
, 1998
"... In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial ..."
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Cited by 96 (9 self)
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In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial is to explain the design choices behind the development of EMPA and how the four features above interact, and to show that a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory has been achieved.
A brief history of process algebra
 Theor. Comput. Sci
, 2004
"... Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The a ..."
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Cited by 59 (1 self)
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Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.
Weak Bisimulation for Fully Probabilistic Processes
, 1999
"... Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisi ..."
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Cited by 56 (8 self)
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Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisimulation for fully probabilistic systems, transition systems where nondeterministic branching is replaced by probabilistic branching. In contrast to the nondeterministic case, both relations coincide. We give an algorithm to decide weak (and branching) bisimulation with a time complexity cubic in the number of states of the fully probabilistic system. This meets the worst case complexity for deciding branching bisimulation in the nondeterministic case. In addition, the relation is shown to be a congruence with respect to the operators of PLSCCS , a lazy synchronous probabilistic variant of CCS. We illustrate that due to these properties, weak bisimulation provides all the crucial ingredients...
Process Algebra for Performance Evaluation
, 2000
"... This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resourcesharing systems  like largescale computers, clientserver architectur ..."
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Cited by 54 (13 self)
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This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resourcesharing systems  like largescale computers, clientserver architectures, networks  can accurately be described using such stochastic specification formalisms.
The Metric Analogue of Weak Bisimulation for Probabilistic Processes
, 2002
"... We observe that equivalence is not a robust concept in the presence of numerical information  such as probabilities  in the model. We develop a metric analogue of weak bisimulation in the spirit of our earlier work on metric analogues for strong bisimulation. We give a fixed point characterization ..."
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Cited by 51 (2 self)
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We observe that equivalence is not a robust concept in the presence of numerical information  such as probabilities  in the model. We develop a metric analogue of weak bisimulation in the spirit of our earlier work on metric analogues for strong bisimulation. We give a fixed point characterization of the metric. This makes available coinductive reasoning principles and allows us to prove metric analogues of the usual algebraic laws for process combinators. We also show that quantitative properties of interest are continuous with respect to the metric, which says that if two processes are close in the metric then observable quantitative properties of interest are indeed close. As an important example of this we show that nearby processes have nearby channel capacities  a quantitative measure of their propensity to leak information.
Metrics for Labelled Markov Processes
, 2003
"... 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 ..."
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Cited by 46 (10 self)
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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 Kantorovich metric.
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 ..."
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Cited by 43 (8 self)
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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.
Refinementoriented probability for CSP
, 1995
"... Jones and Plotkin give a general construction for forming a probabilistic powerdomain over any directedcomplete partial order [Jon90, JP89]. We apply their technique to the failures/divergences semantic model for Communicating Sequential Processes [Hoa85]. The resulting probabilistic model supports ..."
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Cited by 35 (5 self)
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Jones and Plotkin give a general construction for forming a probabilistic powerdomain over any directedcomplete partial order [Jon90, JP89]. We apply their technique to the failures/divergences semantic model for Communicating Sequential Processes [Hoa85]. The resulting probabilistic model supports a new binary operator, probabilistic choice, and retains all operators of CSP including its two existing forms of choice. An advantage of using the general construction is that it is easy to see which CSP identities remain true in the probabilistic model. A surprising consequence however is that probabilistic choice distributes through all other operators; such algebraic mobility means that the syntactic position of the choice operator gives little information about when the choice actually must occur. That in turn leads to some interesting interaction between probability and nondeterminism. A simple communications protocol is used to illustrate the probabilistic algebra, and several sugg...