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13
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 40 (7 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...
Process Algebra with Probabilistic Choice
 In Proceedings of ARTS'99, LNCS 1601
, 1999
"... Published results show that various models may be obtained by combining parallel composition with probability and with or without nondeterminism. In this paper we treat this problem in the setting of process algebra in the form of ACP. First, probabilities are introduced by an operator for the inte ..."
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Cited by 35 (3 self)
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Published results show that various models may be obtained by combining parallel composition with probability and with or without nondeterminism. In this paper we treat this problem in the setting of process algebra in the form of ACP. First, probabilities are introduced by an operator for the internal probabilistic choice. In this way we obtain the Basic Process Algebra with probabilistic choice prBPA.After wards, prBPA is extended with parallel composition to ACP # .Wegive the axiom system for ACP # and a complete operational semantics that preserves the interleaving model for the dynamic concurrent processes. Considering the PAR protocol, a communication protocol that can be used in the case of unreliable channels, we investigate the applicability of ACP # . Using in addition only the priority operator and the preabstraction operator we obtain a recursive specification of the behaviour of the protocol that can be viewed as a Markov chain. 1
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 ..."
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Cited by 15 (4 self)
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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.
Mixing Up Nondeterminism and Probability: a preliminary report
, 1999
"... For a process language with both nondeterministic and probabilistic choice, and a form of failure a transition system is given from which, in a modular way, various operational models corresponding to various interpretations of nondeterminism and probability can be obtained. The effect of failure of ..."
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Cited by 6 (4 self)
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For a process language with both nondeterministic and probabilistic choice, and a form of failure a transition system is given from which, in a modular way, various operational models corresponding to various interpretations of nondeterminism and probability can be obtained. The effect of failure of one component for the system as a whole is treated differently in each interpretation. The same approach is followed for an extension of the language with a parallel operator. The adopted concurrency model is of a distributed nature and assumes that progress is guaranteed if nonfailing components exist. To this end the notion of a takeover of a failing component is incorporated in the transition system. It is shown that the modular way in which the transition system can yield different semantical models applies to this setting as well.
Comparative Semantics for a Process Language With Probabilistic Choice and NonDeterminism
, 1998
"... In this report a comparative semantics is given for a language L p containing probabilistic and nondeterministic choice. The effects of interpreting these operators as local or global are investigated. For three of the possible combinations an operational model and a denotational model are given an ..."
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Cited by 3 (2 self)
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In this report a comparative semantics is given for a language L p containing probabilistic and nondeterministic choice. The effects of interpreting these operators as local or global are investigated. For three of the possible combinations an operational model and a denotational model are given and compared. First models for local probabilistic choice and local nondeterministic choice are given using a generative approach. By adjusting these models slightly models for global probability and local nondeterminism are obtained. Finally models for local probability and global nondeterminism are presented using a stratified approach. For use with the denotational models a construction of a complete ultrametric space of finite multisets is given. 1 Introduction The goal of this paper is to construct comparative semantics for a language combining nondeterminism and probabilistic choice. The main interest is the interplay between these two concepts. Since many of the interesting proper...
Refinement sensitive formal semantics of state machines with persistent choice
 In AVoCS
, 2007
"... Modeling languages usually support two kinds of nondeterminism, an external one for interactions of a system with its environment, and one that stems from underspecification as familiar in models of behavioral requirements. Both forms of nondeterminism are resolvable by composing a system with an e ..."
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Cited by 3 (3 self)
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Modeling languages usually support two kinds of nondeterminism, an external one for interactions of a system with its environment, and one that stems from underspecification as familiar in models of behavioral requirements. Both forms of nondeterminism are resolvable by composing a system with an environment model and by refining underspecified behavior (respectively). Modeling languages usually don’t support nondeterminism that is persistent in that neither the composition with an environment nor refinements of underspecification will resolve it. Persistent nondeterminism is used, e.g., for modeling faulty systems. We present a formal semantics for UML state machines enriched with an operator “persistent choice ” that models persistent nondeterminism. This semantics is based on abstract models – µautomata with a novel refinement relation – and a sound threevalued satisfaction relation for properties expressed in the µcalculus. Keywords: modeling language, nondeterminism, µcalculus, 3valued satisfaction, formal semantics
Time and Probability in Process Algebra
 PROCEEDINGS OF AMAST 2000, VOLUME 1816 OF LNCS
, 2000
"... In the paper we present an ACPlike process algebra which can be used to model both probabilistic and time behaviour of parallel systems. This process algebra is obtained by extension of untimed probabilistic process algebra with constructors that allow the explicit specification of timing aspec ..."
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Cited by 2 (0 self)
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In the paper we present an ACPlike process algebra which can be used to model both probabilistic and time behaviour of parallel systems. This process algebra is obtained by extension of untimed probabilistic process algebra with constructors that allow the explicit specification of timing aspects. In this paper we concentrate on giving axioms and deduction rules for these constructors. We give two probabilistic process algebras with discrete time. The first one only manipulates with processes that may be initialized within the current time slice or may delay a finite and fixed number of time slices. Later, we add processes whose execution can be postponed for an arbitrary number of time slices.
Process Algebra Having Inherent Choice: Revised Semantics for Concurrent Systems
, 2007
"... Process algebras are standard formalisms for compositionally describing systems by the dependencies of their observable synchronous communication. In concurrent systems, parallel composition introduces resolvable nondeterminism, i.e., nondeterminism that will be resolved in later design phases or by ..."
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Cited by 1 (1 self)
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Process algebras are standard formalisms for compositionally describing systems by the dependencies of their observable synchronous communication. In concurrent systems, parallel composition introduces resolvable nondeterminism, i.e., nondeterminism that will be resolved in later design phases or by the operating system. Sometimes it is also important to express inherent nondeterminism for equal (communication) labels. Here, we give operational and axiomatic semantics to a process algebra having a parallel operator interpreted as concurrent and having a choice operator interpreted as inherent, not only w.r.t. different, but also w.r.t. equal nextstep actions. In order to handle the different kinds of nondeterminism, the operational semantics uses µautomata as underlying semantical model. Soundness and completeness of our axiom system w.r.t. the operational semantics is shown.
c ○ 2004 BCS Refinementoriented probability for CSP
"... Abstract. 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 mode ..."
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Abstract. 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 suggestions are made for accommodating and controlling nondeterminism when probability is present. Keywords: Probability, concurrency, nondeterminism, refinement, CSP. 1.