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**1 - 2**of**2**### On Coinduction and Quantum Lambda Calculi∗

"... In the ubiquitous presence of linear resources in quantum computation, program equivalence in linear contexts, where programs are used or executed once, is more important than in the classical setting. We introduce a linear contextual equivalence and two notions of bisimilarity, a state-based and a ..."

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In the ubiquitous presence of linear resources in quantum computation, program equivalence in linear contexts, where programs are used or executed once, is more important than in the classical setting. We introduce a linear contextual equivalence and two notions of bisimilarity, a state-based and a distribution-based, as proof techniques for reasoning about higher-order quantum programs. Both notions of bisimilarity are sound with respect to the linear contextual equivalence, but only the distribution-based one turns out to be complete. The completeness proof relies on a characterisation of the bisimilarity as a testing equivalence.

### Logical Characterizations of Simulation and Bisimulation for Fuzzy Transition Systems

"... Simulations and bisimulations are known to be useful for abstracting and comparing formal systems, and they have recently been introduced into fuzzy systems. In this study, we provide sound and complete logical characterizations for simulation and bisimulation, which are defined over fuzzy labeled t ..."

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Simulations and bisimulations are known to be useful for abstracting and comparing formal systems, and they have recently been introduced into fuzzy systems. In this study, we provide sound and complete logical characterizations for simulation and bisimulation, which are defined over fuzzy labeled transition systems via two variants of the Hennessy-Milner Logic. The logic for character-izing fuzzy simulation has neither negation nor disjunction, which is very differ-ent from the well-known logical characterizations of probabilistic simulations, although the completeness proofs of our characterization results are inspired by relevant research in probabilistic concurrency theory. The logic for characteriz-ing fuzzy bisimulation also deviates from that for probabilistic bisimulations.