Behavioural equivalences on open systems are usually defined by comparing system behaviour in all environments. Due to this “universal” quantification over the possible hosting environments, such equivalences are often difficult to check in a direct way. Here, working in the setting of process calculi, we introduce a hierarchy of behavioural equivalences for open systems, building on a previous...

We show that derived equivalences preserve the homotopy type of the (cohomological) Hochschild complex as a B∞-algebra. More generally, we prove that, as an object of the homotopy category of B∞-algebras, the Hochschild complex is contravariant with respect to fully faithful derived tensor functors. We also show that the Hochschild complexes of a Koszul algebra and its dual are homotopy equival...

This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in relative situation over noncentral, noncommutative, nonsemisimple base ring, as announced Section 0.4 arXiv:0708.3398. We prove Poincare-Birkhoff-Witt theorem this context and construct triangulated equivalences derived duality. The between ring differential operators de Rham DG-algebra, with functions is th...

We present a bicategorical perspective on derived Morita theory for rings, DG algebras, and spectra. This perspective draws a connection between Morita theory and the bicategorical Yoneda Lemma, yielding a conceptual unification of Morita theory in derived and bicategorical contexts. This is motivated by study of Rickard’s theorem for derived equivalences of rings and of Morita theory for ring ...

The Gamma model is a minimal programming notation based on the chemical reaction metaphor. Hankin, Le M etayer, and Sands derived a Calculus of Gamma Programs adding two operators to the notation: the parallel and sequential composition operators. In this paper we address some compositional problems due to the semantics of the parallel operator for which we propose an alternative semantics as a...

The optimization of computing systems that incorporate Boolean-circuit-based computing equipment must be expressed at some level in Boolean behaviors and operations. Boolean behaviors and operations are part of a larger family of logics -the logic of sentences, also known as the "sentential calculus". Two logics are implicationally equivalent if the axioms and inference rules of each imply the ...

There is recent interest in compressing data sets for non-sequential settings, where lack of obvious orderings on their data space, require notions of data equivalences to be considered. For example, Varshney & Goyal (DCC, 2006) considered multiset equivalences, while Choi & Szpankowski (IEEE Trans. IT, 2012) considered isomorphic equivalences in graphs. Here equivalences are considered under a...