We study a process calculus which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch’s probabilistic automata. We consider various strong and weak behavioral equivalences, and we provide complete axiomatizations for finite-state processes, restricted to guarded definitions in case of the weak equivalences. We conjecture that in the general case of unguard...

In this paper we prove an existence of some type of equivalences between triangulated categories of singularities for varieties of different dimensions. This class of equivalences generalizes so called Knörrer periodicity. As consequence we get equivalences between categories of D-branes of type B on Landau-Ginzburg models of different dimensions.

In the context of CCSK, a reversible extension CCS, we study observational equivalences that distinguish forward moves from backward ones. We present refinement notion forward-reverse bisimilarity and show it coincides with barbed congruence. also set sound axioms allowing one to reason equationally on process equivalences.

The equivalence between a monoidal category and a strict one has been proved by some authors such as Nguyen Duy Thuan [8], Christian Kassel [2], Peter Schauenburg [7]. In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M -functors and M morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic chara...