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Characterising testing preorders for finite probabilistic processes
 In LICS’07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, CA
"... In 1992 Wang & Larsen extended the may and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative cha ..."
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In 1992 Wang & Larsen extended the may and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both problems for finite processes with silent moves. It characterises the may preorder in terms of simulation, and the must preorder in terms of failure simulation. It also gives a characterisation of both preorders using a modal logic. Finally it axiomatises both preorders over a probabilistic version of CSP. 1.
Towards a quantum process algebra
"... Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of algorithms making use of quantum principles must take into a ..."
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Cited by 24 (0 self)
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Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. This paper aims at defining a high level language allowing the description of classical and quantum programming, and their cooperation. Since process algebras provide a framework to model cooperating computations and have well defined semantics, they have been chosen as a basis for this language. Starting with a classical process algebra, this paper explains how to transform it for including quantum computation. The result is a quantum process algebra with its operational semantics, which can be used to fully describe quantum algorithms in their classical context. 1
A process algebraic approach to concurrent and distributed quantum computation: operational semantics
 In QPL 2004
"... Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and distributed quantum computations, as well as quantum communicatio ..."
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Cited by 24 (1 self)
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Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and distributed quantum computations, as well as quantum communication protocols, quantum to quantum communications which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined, named QPAlg for Quantum Process Algebra, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts. On the quantum side, QPAlg provides quantum variables, operations on quantum variables (unitary operators and measurement observables), as well as new forms of communications involving the quantum world. The operational semantics makes sure that these quantum objects, operations and communications operate according to the postulates of quantum mechanics.
A Uniform Framework for Modeling Nondeterministic, Probabilistic, Stochastic, or Mixed Processes and their Behavioral Equivalences
, 2013
"... Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a onestep statetostate reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pai ..."
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Cited by 9 (4 self)
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Labeled transition systems are typically used as behavioral models of concurrent processes. Their labeled transitions define a onestep statetostate reachability relation. This model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label. The state reachability distribution is a function mapping each possible target state to a value that expresses the degree of onestep reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture wellknown models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. They can be defined on ULTraS by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multistep computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models except when nondeterminism and probability/stochasticity coexist; then new equivalences pop up.
A Probabilistic Branching Bisimulation for Quantum Processes. quantph/0508116, 2005. [Lal06] [LGP06] Marie Lalire. Développement d’une notation alorithmique pour le calcul quantique
, 2006
"... Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and distributed quantum computations, as well as quantum communicatio ..."
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Cited by 6 (0 self)
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Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and distributed quantum computations, as well as quantum communication protocols, quantum to quantum communications which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts. Based upon an operational semantics which makes sure that quantum objects, operations and communications operate according to the postulates of quantum mechanics, a probabilistic branching bisimulation is defined among processes considered as having the same behavior. 1
Mutation Testing from Probabilistic and Stochastic Finite State Machines
 Journal of Systems and Software
, 2009
"... Specification mutation involves mutating a specification, and for each mutation a test is derived that distinguishes the behaviours of the mutated and original specifications. This approach has been applied with finite state machines based models. This paper extends mutation testing to finite state ..."
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Specification mutation involves mutating a specification, and for each mutation a test is derived that distinguishes the behaviours of the mutated and original specifications. This approach has been applied with finite state machines based models. This paper extends mutation testing to finite state machine models that contain nonfunctional properties. The paper describes several ways of mutating a finite state machine with probabilities (PFSM) or stochastic time (PSFSM) attached to their transitions and shows how test sequences that distinguish between them and their mutants can be generated. Testing then involves applying each test sequence multiple times, observing the resultant output sequences and using results from statistical sampling theory in order to compare the observed frequency of each output sequence with that expected. Key words: mutation testing; probabilities; stochastic time; specification mutation 1
Implementation relations for stochastic finite state machines
 In 3rd European Performance Engineering Workshop, EPEW’06, LNCS 3964
, 2006
"... Abstract. We present a timed extension of the classical finite state machines model where time is introduced in two ways. On the one hand, timeouts can be specified, that is, we can express that if an input action is not received before a fix amount of time then the machine will change its state. On ..."
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Abstract. We present a timed extension of the classical finite state machines model where time is introduced in two ways. On the one hand, timeouts can be specified, that is, we can express that if an input action is not received before a fix amount of time then the machine will change its state. On the other hand, we can associate time with the performance of actions. In this case, time will be given by means of random variables. Intuitively, we will not have conditions such as “the action a takes t time units to be performed ” but conditions such as “the action a will be completed before time t with probability p. ” In addition to introducing the new language, we present several conformance relations to relate implementations and specifications that are defined in terms of our new notion of stochastic finite state machine. 1
A hierarchy of equivalences for probabilistic processes. In:
 28th IFIP Int. Conf. on Formal Techniques for Networked and Distributed Systems, FORTE’08, LNCS 5048.
, 2008
"... Abstract. We study several process equivalences on a probabilistic process algebra. First, we define an operational semantics. Afterwards we introduce the notion of passing a test with a probability. We consider three families of tests according to the intended behavior of an external observer: Rea ..."
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Abstract. We study several process equivalences on a probabilistic process algebra. First, we define an operational semantics. Afterwards we introduce the notion of passing a test with a probability. We consider three families of tests according to the intended behavior of an external observer: Reactive (sequential tests), generative (branching tests), and limited generative (equitable branching tests). For each of these families we define three predicates over processes and tests (maypass, mustpass, passp ) which induce three equivalences. Finally, we relate these nine equivalences and provide either alternative characterizations or fully abstract denotational semantics. These semantic frameworks cover from simple traces to probabilistic acceptance trees.
Derivation of a Suitable Finite Test Suite for Customized Probabilistic Systems⋆
"... Abstract. In order to check the conformance of an IUT (implementation under test) with respect to a specification, it is not feasible, in general, to test the whole set of IUT available behaviors. In some situations, testing the behavior of the IUT assuming that it is stimulated by a given usage m ..."
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Abstract. In order to check the conformance of an IUT (implementation under test) with respect to a specification, it is not feasible, in general, to test the whole set of IUT available behaviors. In some situations, testing the behavior of the IUT assuming that it is stimulated by a given usage model is more appropriate. Specifically, if we consider that specifications and usage models are defined in probabilistic terms, then by applying a finite set of tests to the IUT we can compute a relevant metric: An upper bound of the probability that a user following the usage model finds an error in the IUT. We also present a method to find an optimal (with respect to the number of inputs) set of tests that minimizes that upper bound. 1