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Hyperproperties are a modern specification paradigm that extends trace properties to express properties of sets of traces. Temporal logics for hyperproperties studied in the literature, including HyperLTL, assume a synchronous semantics and enjoy a decidable model checking problem. In this paper, we introduce two asynchronous and orthogonal extensions of HyperLTL, namely Stuttering HyperLTL (HyperLTLS) and Context HyperLTL (HyperLTLC). Both of these extensions are useful, for instance, to formulate asynchronous variants of information-flow security properties. We show that for these logics, model checking is in general undecidable. On the positive side, for each of them, we identify a fragment with a decidable model checking that subsumes HyperLTL and that can express meaningful asynchronous requirements. Moreover, we provide the exact computational complexity of model checking for these two fragments which, for the HyperLTLS fragment, coincides with that of the strictly less expressive logic HyperLTL.
Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically intereste
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Given a field K, a quadratic extension field L is an extension of K that can be generated from K by adding a root of a quadratic polynomial with coefficients in K. This paper shows how ACL2(r) can be used to reason about chains of quadratic extension
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