The asymptotic normality of the sample mean of iid rv's is equivalent to the well known conditions of Levy and Feller. More recently, additional equivalences have been developed in terms of the quantile function (qf). And other useful probabilistic equivalences could be cited. But the asymptotic normality cited above is also equivalent to appropriately phrased consistency of the sample second m...

Probabilistic automata (PA) [20] have been successfully applied in the formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on PCTL [11] and its extension PCTL [4]. Various behavioral equivalences are proposed for PAs, as a powerful tool for abstraction and compositio...

We propose a generic method for deciding semantic equivalences between pushdown automata and finite-state automata. The abstract part of the method is applicable to every process equivalence which is a right PDA congruence. Practical usability of the method is demonstrated on selected equivalences which are conceptual representatives of the whole spectrum. In particular, special attention is de...

Throughout this paper k denotes an algebraically closed field, and all algebras considered here are assumed to be basic, connected, finite-dimensional k-algebras with identity. For an algebra Λ, we denote by modΛ and by modΛ the category of finitedimensional (right) Λ-modules and its stable category, respectively. Recall that for two algebras Λ and Π, an equivalence modΛ → modΠ is called a stab...

We check that there exists a structure of model category on the category of flows whose weak equivalences are the S-homotopy equivalences. This model structure is simplicial, but not topological.