Logics for reasoning about quantum states and their evolution have been given in the literature. In this paper we consider Quantum Computation Tree Logic (QCTL), which adds temporal modalities to exogenous quantum propositional logic. We give a sound and complete axiomatization of QCTL and combine the standard CTL model-checking algorithm with the dEQPL model-checking algorithm to obtain a model-checking algorithm for QCTL. Finally we illustrate the use of the logic by reasoning about the BB84 key distribution protocol.
Abstract. Communication protocols in distributed systems often specify the roles of the parties involved in the communications, namely for enforcing security policies or task assignment purposes. Ensuring that implementations follow role-based protocol specifications is challenging, especially in scenarios found, e.g., in business processes and web applications, where multiple peers are involved, single peers impersonate several roles, or single roles are carried out by several peers. We present a type-based analysis for statically verifying role-based multi-party interactions, based on a simple ⌅-calculus model and prior work on conversation types. Our main result ensures that well-typed systems follow the rolebased protocols prescribed by the types, including systems where roles are flexibly assigned to processes.
Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation, combining types with logical formulae that may refer to program values and can constrain types using arbitrary predicates. We present a pi calculus with assume and assert operations, typed using a session discipline that incorporates refinement formulae written in a fragment of Multiplicative Linear Logic. Our original combination of session and refinement types, together with the well established benefits of linearity, allows very fine-grained specifications of communication protocols in which refinement formulae are treated as logical resources rather than persistent truths.
Logics for reasoning about quantum states have been given in the literature. In this paper, we extend one such logic with temporal constructs mimicking the standard computational tree logic used to reason about classical transition systems. We investigate the model-checking problem for this temporal quantum logic and illustrate its use by reasoning about the BB84 key distribution protocol.
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