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16
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 14 (3 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.
A Theory of Testing for Markovian Processes
 in Proc. of the 11th Int. Conf. on Concurrency Theory (CONCUR 2000), LNCS 1877:305319, State College (PA
, 2000
"... . We present a testing theory for Markovian processes in order to formalize a notion of efficiency which may be useful for the analysis of soft real time systems. Our Markovian testing theory is shown to enjoy close connections with the classical testing theory of De NicolaHennessy and the proba ..."
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Cited by 13 (5 self)
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. We present a testing theory for Markovian processes in order to formalize a notion of efficiency which may be useful for the analysis of soft real time systems. Our Markovian testing theory is shown to enjoy close connections with the classical testing theory of De NicolaHennessy and the probabilistic testing theory of CleavelandSmolka et al. The Markovian testing equivalence is also shown to be coarser than the Markovian bisimulation equivalence. A fully abstract characterization is developed to ease the task of establishing testing related relationships between Markovian processes. It is then demonstrated that our Markovian testing equivalence, which is based on the (easier to work with) probability of executing a successful computation whose average duration is not greater than a given amount of time, coincides with the Markovian testing equivalence based on the (more intuitive) probability of reaching success within a given amount of time. Finally, it is shown that...
Algebraic Theory of Probabilistic and Nondeterministic Processes
 PROCEEDINGS OF THE WORKSHOP
, 2001
"... In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL, which is a probabilistic extension of EPL (Algebraic Theory of Processes, M. Hennessy) that maintains nondeterminism.We have ..."
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Cited by 12 (0 self)
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In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL, which is a probabilistic extension of EPL (Algebraic Theory of Processes, M. Hennessy) that maintains nondeterminism.We have
Testing Semantics for Probabilistic LOTOS
, 1995
"... In this paper we present a probabilistic extension of LOTOS which is upward compatible with LOTOS. We present testing semantics for the reactive and generative models described in [vGSST90]. While there is a certain lose of the meaning of probabilities in the reactive model, testing with probabilist ..."
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Cited by 11 (7 self)
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In this paper we present a probabilistic extension of LOTOS which is upward compatible with LOTOS. We present testing semantics for the reactive and generative models described in [vGSST90]. While there is a certain lose of the meaning of probabilities in the reactive model, testing with probabilistic tests proves to be too strong, because it does not relate behavior expressions which we expect to be equivalent. This is why we introduce the limited generative model, where tests are not allowed to have explicit probabilities. We give a fully abstract characterization for the reactive model, while we give alternative characterizations (based on a set of essential tests) for the generative and limited generative models. We also present some algebraic laws for each of the models, including some laws which establish the difference between the three models.
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...
A Process Algebra for Probabilistic and Nondeterministic Processes
 Information Processing Letters
, 2001
"... In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL , which is a probabilistic extension of EPL that maintains nondeterminism. ..."
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Cited by 7 (2 self)
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In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL , which is a probabilistic extension of EPL that maintains nondeterminism.
An Example of Performance Evaluation by using the Stochastic Process Algebra: ROSA
 Cheju Island, South Korea
, 2000
"... We present an algebraic language for the description of probabilistic and nondeterministic processes, which allows us to evaluate performance indexes as well as to check some temporal requirements: ROSA (Reasoning On Stochastic Algebras). As application, we analyse the Alternating Bit Protocol obta ..."
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Cited by 3 (2 self)
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We present an algebraic language for the description of probabilistic and nondeterministic processes, which allows us to evaluate performance indexes as well as to check some temporal requirements: ROSA (Reasoning On Stochastic Algebras). As application, we analyse the Alternating Bit Protocol obtaining the average time to send a message, considering that channels may fail with a known probability.
Taking Chances on  and fail: Extending Strong and Probabilistic Bisimulation
, 1999
"... For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed. As one can interpret recovery from failure with respect to nondeterministic and probabilistic choice in various ways, a single transition sy ..."
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Cited by 2 (1 self)
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For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed. As one can interpret recovery from failure with respect to nondeterministic and probabilistic choice in various ways, a single transition system gives rise to several operational models. A uniform way to abstract the `first steps' underlies, for each of these models, the definition of the proposed bisimulation. This bisimulation specializes to ParkMilner bisimulation for the nonprobabilistic fragment of the language on the one hand, and to LarsenSkou bisimulation for the deterministic/probabilistic part of the language, on the other hand. Furthermore, a conditional congruence result is obtained. 1 Introduction Understanding the interplay of nondeterminacy and probability is a key issue in the development of formal techniques for specification and validation of probabilistic programs and protocols. In this paper we study a pr...
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].
Fair Testing Through Probabilistic Testing
, 1999
"... In this paper we define a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to define a probabilistic semantics in such a way that two nonprobabilistic processes are fair equivalent iff any probabilistic version of both processes are equiv ..."
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Cited by 2 (1 self)
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In this paper we define a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to define a probabilistic semantics in such a way that two nonprobabilistic processes are fair equivalent iff any probabilistic version of both processes are equivalent in our probabilistic testing semantics. In order to get this result we define a simple probabilistic must semantics by saying that a probabilistic process must pass a test iff the probability with which the process passes the test equals 1. Finally, we present an algorithm for deciding whether the probability with which a finitestate process passes a finitestate test equals 1. Alternatively, this algorithm can be used for computing whether a finitestate process fairly passes a finitestate test. Keywords: Testing semantics, fair testing, probabilistic processes. 1. INTRODUCTION Formal models of concurrency have been proved to be very useful to properly specify concurrent and distr...