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Weak distribution bisimilarity is an equivalence notion on probabilistic automata, originally proposed for Markov automata. It has gained some popularity as the coarsest behavioral equivalence enjoying valuable properties like preservation of trace distribution equivalence and compositionality. This holds in the classical context of arbitrary schedulers, but it has been argued that this class of schedulers is unrealistically powerful. This paper studies a strictly coarser notion of bisimilarity, which still enjoys these properties in the context of realistic subclasses of schedulers: Trace distribution equivalence is implied for partial information schedulers, and compositionality is preserved by distributed schedulers. The intersection of the two scheduler classes thus spans a coarser and still reasonable compositional theory of behavioral semantics. [ABSTRACT FROM AUTHOR]

We propose a Curry-Howard correspondence between a language for programming multiparty sessions and a generalisation of Classical Linear Logic (CLL). In this framework, propositions correspond to the local behaviour of a participant in a multiparty session type, proofs to processes, and proof normalisation to executing communications. Our key contribution is generalising duality, from CLL, to a new notion of n-ary compatibility, called coherence. Building on coherence as a principle of compositionality, we generalise the cut rule of CLL to a new rule for composing many processes communicating in a multiparty session. We prove the soundness of our model by showing the admissibility of our new rule, which entails deadlock-freedom via our correspondence. [ABSTRACT FROM AUTHOR]

Regular expressions ( RE) are an algebraic formalism for expressing regular languages, widely used in string search and as a specification language in verification. In this paper, we introduce and investigate visibly rational expressions ( VRE), an extension of RE for the class of visibly pushdown languages ( VPL). We show that VRE capture precisely the class of VPL. Moreover, we identify an equally expressive fragment of VRE which admits a quadratic time compositional translation into the automata acceptors of VPL. We also prove that, for this fragment, universality, inclusion and language equivalence are EXPTIME-complete. Finally, we provide an extension of VRE for VPL over infinite words. [ABSTRACT FROM AUTHOR]