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Equational axioms for probabilistic bisimilarity
 IN PROCEEDINGS OF 9TH AMAST, LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending ..."
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Cited by 18 (0 self)
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This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (#)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity.
Compositional reasoning for probabilistic finitestate behaviors
 In Processes, Terms and Cycles: Steps on the Road to Infinity, Essays Dedicated to Jan Willem Klop, on the Occasion of His 60th Birthday, LNCS 3838
, 2005
"... Abstract. We study a process algebra which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s simple probabilistic automata. We consider strong bisimulation and observational equivalence, and provide complete axiomatizations for a language that includes para ..."
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Cited by 17 (4 self)
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Abstract. We study a process algebra which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s simple probabilistic automata. We consider strong bisimulation and observational equivalence, and provide complete axiomatizations for a language that includes parallel composition and (guarded) recursion. The presence of the parallel composition introduces various technical difficulties and some restrictions are necessary in order to achieve complete axiomatizations. 1
Duality for Labelled Markov Processes
"... Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a `universal' LMP as the spectrum of a commutative C # algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the univ ..."
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Cited by 10 (1 self)
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Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a `universal' LMP as the spectrum of a commutative C # algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the universal LMP as the set of homomorphims from an ordered commutative monoid of labelled trees into the multiplicative unit interval. This yields a simple semantics for LMPs which is fully abstract with respect to probabilistic bisimilarity. We also consider LMPs with entry points and exit points in the setting of iteration theories. We define an iteration theory of LMPs by specifying its categorical dual: a certain category of C*algebras. We find that the basic operations for composing LMPs have simple definitions in the dual category.
NMSPA: A NonMarkovian Model for Stochastic Processes
, 2000
"... In this paper we introduce a new Stochastic Process Algebra: NMSPA. This new language presents the usual features of stochastic models but probability distributions are not restricted to be exponential. This fact increases the expressive power of the language in several ways. For example, we can sp ..."
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Cited by 8 (0 self)
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In this paper we introduce a new Stochastic Process Algebra: NMSPA. This new language presents the usual features of stochastic models but probability distributions are not restricted to be exponential. This fact increases the expressive power of the language in several ways. For example, we can specify actions that can be executed with probability 1 in a finite amount of time, socalled passive actions fall in a natural way inside our framework, urgency of internal actions can be expressed, etc. In order to define an interleaving semantics for the parallel operator, we benefit from ideas used in timed process algebras. Our operational transitions include information about the time when actions can be executed, as well as the random variable associated with them. We provide our language with a notion of strong bisimulation which takes into account urgency of internal transitions. Finally, we specify the Alternating Bit Protocol. This is a very simple communication protocol where th...
Deriving syntax and axioms for quantitative regular behaviours
, 2009
"... We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions ar ..."
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Cited by 7 (4 self)
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We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA’s) and Milner (on regular behaviours and finite LTS’s), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new ones, for many different kinds of probabilistic systems.
Axiomatization of trace semantics for stochastic nondeterministic processes. Quantitative Evaluation of Systems
 In Proceedings of QEST
, 2004
"... We give a complete axiomatization of trace distribution precongruence for probabilistic nondeterministic processes based on a process algebra that includes internal behavior and recursion. The axiomatization is given for two different semantics of the process algebra that are consistent with the alt ..."
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Cited by 4 (1 self)
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We give a complete axiomatization of trace distribution precongruence for probabilistic nondeterministic processes based on a process algebra that includes internal behavior and recursion. The axiomatization is given for two different semantics of the process algebra that are consistent with the alternating model of Hansson and the nonalternating model of Segala, respectively. It is shown that the two semantics coincide up to trace distribution precongruence. 1.
An Axiomatization of Probabilistic Testing
, 1999
"... In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics defined in [19]. ..."
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Cited by 2 (1 self)
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In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics defined in [19].
Combining Timed Coordination Primitives and Probabilistic Tuple Spaces ⋆
"... Abstract. In this paper we present an integration of PLinda, a probabilistic extension of Linda, and StoKlaim, a stochastic extension of KLAIM. In the resulting language, StoPKlaim, the execution time of coordination primitives is modeled by means of exponentially distributed random variables, as in ..."
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Cited by 1 (1 self)
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Abstract. In this paper we present an integration of PLinda, a probabilistic extension of Linda, and StoKlaim, a stochastic extension of KLAIM. In the resulting language, StoPKlaim, the execution time of coordination primitives is modeled by means of exponentially distributed random variables, as in StoKlaim, the choice of the primitive to be executed among conflicting ones is thus resolved by the race condition principle, and the choice of the tuple to be retrieved by a single input/read operation in case of multiple matching tuples is governed by the weightbased probabilistic access policy of PLinda. The language represents a natural development and integration of previous results of the SENSORIA Project in the area of probabilistic and timestochastic extensions of Tuple Space based coordination languages. The formal operational semantics of StoPKlaim is presented and an example of modeling is provided. 1
Testing Semantics for a ProbabilisticTimed Process Algebra
, 1997
"... In this paper we present a probabilistictimed process algebra, which tries to unify the best solutions of previous probabilistic and timed algebras. We provide an operational semantics for the new language (PTPA), and from this operational semantics we define a testing semantics based on the probab ..."
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In this paper we present a probabilistictimed process algebra, which tries to unify the best solutions of previous probabilistic and timed algebras. We provide an operational semantics for the new language (PTPA), and from this operational semantics we define a testing semantics based on the probability with which processes pass tests. Afterwards the induced testing equivalence is operationally characterized by probabilistic timed traces.