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**11 - 18**of**18**### Testing Probabilistic Processes: Can Random Choices Be Unobservable?

, 907

"... Abstract. A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the internal choice is quantified with probabilities. Howeve ..."

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Abstract. A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the internal choice is quantified with probabilities. However, ever since probabilities have been introduced in process semantics, it has been a challenge to preserve the unobservability of the random choice, while not violating the other laws of process theory and probability theory. This paper addresses this problem. It proposes two semantics for processes where the internal nondeterminism has been quantified with probabilities. The first one is based on the notion of testing, i.e. interaction between the process and its environment. The second one, the probabilistic ready trace semantics, is based on the notion of observability. Both are shown to coincide. They are also preserved under the standard operators. 1

### Extending Refusal Testing by Stochastic Refusals for f or Testing Non-deterministic Non deterministic Systems

"... Testing is a validation activity used to check the system’s correctness with respect to the specification. In this context, test based on refusals is studied in theory and tools are effectively constructed. This paper addresses, a formal testing based on stochastic refusals graphs (SRG) in order to ..."

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Testing is a validation activity used to check the system’s correctness with respect to the specification. In this context, test based on refusals is studied in theory and tools are effectively constructed. This paper addresses, a formal testing based on stochastic refusals graphs (SRG) in order to test stochastic system represented by maximality-based stochastic labeled transition systems (MSLTS). First, we propose a framework to generate SRGs from MSLTSs. Second, we present a new technique to generate automatically a canonical tester from stochastic refusal graph and conformance relation confSRG. Finally, implementation is proposed and the application of our approach is shown by an example.

### semantics

"... We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of quantum state; in particular, quantum ..."

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We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems.

### Under consideration for publication in Math. Struct. in Comp. Science Types and Typechecking for Communicating Quantum Processes

, 2004

"... We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of quantum state; in particular, quantum ..."

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We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We also define a typechecking algorithm and prove that it is sound and complete with respect to the type system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems. 1.

### unknown title

"... A process algebraic approach to concurrent and distributed quantum computation: operational semantics ..."

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A process algebraic approach to concurrent and distributed quantum computation: operational semantics

### Testing from a Stochastic Timed System with a Fault Model

, 2008

"... In this paper we present a method for testing a system against a non-deterministic stochastic finite state machine. As usual, we assume that the functional behaviour of the system under test (SUT) is deterministic but we allow the timing to be nondeterministic. We extend the state counting method of ..."

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In this paper we present a method for testing a system against a non-deterministic stochastic finite state machine. As usual, we assume that the functional behaviour of the system under test (SUT) is deterministic but we allow the timing to be nondeterministic. We extend the state counting method of deriving tests, adapting it to the presence of temporal requirements represented by means of random variables. The notion of conformance is introduced using an implementation relation considering temporal aspects and the limitations imposed by a black-box framework. We propose an algorithm for generating a test suite that determines the conformance of a deterministic SUT with respect to a non-deterministic specification. We show how previous work on testing from stochastic systems can be encoded into the framework presented in this paper as an instantiation of our parameterized implementation relation. In this setting, we use a notion of conformance up to a given confidence level.

### Under consideration for publication in Math. Struct. in Comp. Science Relations among Quantum Processes:

, 2005

"... Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, ..."

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Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, communications over quantum channels 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. This notation 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, an equivalence is defined among process states considered as having the same behavior. This equivalence is a probabilistic branching bisimulation. From this relation, an equivalence on processes is defined. However, it is not a congruence because it is not preserved by parallel composition. 1.