Axiomatizing Probabilistic Processes: ACP with Generative Probabilities

  title={Axiomatizing Probabilistic Processes: ACP with Generative Probabilities},
  author={Jos C. M. Baeten and Jan A. Bergstra and Scott A. Smolka},
  journal={Inf. Comput.},
This paper is concerned with finding complete axiomatizations of probabilistic processes. We examine this problem within the context of the process algebra ACP and obtain as our end-result the axiom system prACP I −- , a probabilistic version of ACP which can be used to reason algebraically about the reliability and performance of concurrent systems. Our goal was to introduce probability into ACP in as simple a fashion as possible. Optimally, ACP should be the homomorphic image of the… 

Process Algebra with Probabilistic Choice

  • S. Andova
  • Computer Science, Mathematics
  • 1999
This paper treats the problem of combining parallel composition with probability and with or without non-determinism in the setting of process algebra in the form of ACP to obtain the Basic Process Algebra with probabilistic choice prBPA and the axiom system for ACP+π.

Algebraic theory of probabilistic processes

  • M. Núñez
  • Computer Science, Mathematics
    J. Log. Algebraic Methods Program.
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Probabilistic process algebra and strategic interleaving

A Probabilistic version of ACP is presented that rests on the principle that probabilistic choices are always resolved before choices involved in alternative composition and parallel composition are resolved and a form of interleaving in which parallel processes are interleaved according to what is known as a process-scheduling policy in the field of operating systems is extended.

Process algebra with interleaving probabilistic parallel composition

A probabilistic version of the axiom system A CP appropriate for the (algebraic) formal description of pIobabilisti.c processes is presented and Probabilistic (strong) bisimulation as proposed by Larsen and Skou is a congruence and the soundness and completeness of the presented term model are proved.

Probabilistic Congruence for Semistochastic Generative Processes

Most of operations of the probabilistic process algebras studied in the literature are captured by the rule format, which, therefore, has practical applications.

An Axiomatization of Strong Distribution Bisimulation for a Language with a Parallel Operator and Probabilistic Choice

  • J. F. GrooteE. Vink
  • Computer Science
    From Software Engineering to Formal Methods and Tools, and Back
  • 2019
Distributions rather than states are the leading ingredients for building the semantics and the accompanying equational theory, for which soundness and completeness are established.

Axioms for Probability and Nondeterminism

Taking Chances on k and fail : Extending Strong and Probabilistic

For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed, and a conditional congruence result is obtained.

Probabilistic Information Flow in a Process Algebra

A process algebraic approach for extending to the probabilistic setting the classical logical information flow analysis of computer systems and a notion of probabilism bisimulation in order to define classical security properties, such as nondeterministic noninterference (NNI) and nondeducibility on compositions (NDC), in the probablistic setting.



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The nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given explicitly, to obtain a calculus, PCCS, for reasoning about communicating Probabilistic processes.

Testing Preorders for Probabilistic Processes

The theory of testing is extended to substochastic processes, in which the sum of the probabilities of a process's outgoing transitions may be strictly less than 1, with the deficit representing the process' capacity for undefined behavior.

Equivalences, Congruences, and Complete Axiomatizations for Probabilistic Processes

It is shown that, unlike nondeterministic transition systems, “maximality” of traces and failures does not increase the distinguishing power of trace and failure equivalence, respectively.

Compositional Verification of Probabilistic Processes

This study identifies a new probabilistic logic, which is needed in order to support decomposition, and offers complete axiomatizations for both the calculus and the logic.

Reactive, Generative and Stratified Models of Probabilistic Processes

Three models of probabilistic processes, namely, reactive, generative, and stratified, are investigated within the context of PCCS, an extension of Milner′s SCCS in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1.

A Synchronous Calculus of Relative Frequency

A weighted synchronous calculus is presented that can be interpreted as reasoning over probabilistic processes and the notion of dominance is added, shown to be dual to that of “zero probability” and used to construct arbitrary priority structures.

Specification and refinement of probabilistic processes

  • B. JonssonK. Larsen
  • Computer Science
    [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
  • 1991
A formalism for specifying probabilistic transition systems, which constitute a basic semantic model for description and analysis of reliability aspects of concurrent and distributed systems, is presented and it is shown that it is analogous to the extension from processes to modal transition systems.

Foundations of Compositional Program Refinement - Safety Properties

  • R. Gerth
  • Computer Science
    REX Workshop
  • 1989
This paper develops a foundation for refinement of parallel programs that may synchronously communicate and/or share variables; programs rendered as 1st order transition systems and shows that they yield assertional methods for refinement that resemble the methods used in Z. Manna and A. Pnueli's temporal logic proof system.

Asynchronous communication in process algebra

The aim is to develop a process theory that can be regarded as a kernel for languages based on asynchronous communication, like data flow, concurrent logic languages, and concurrent constraint programming.