Probabilistic classifiers are developed by assuming generative models which are product distributions over the original attribute space (as in naive Bayes) or more involved spaces (as in general Bayesian networks). While this paradigm has been shown experimentally successful on real world applications, despite vastly simplified probabilistic assumptions, the question of why these approaches wor...

We propose decision algorithms for bisimulation relations defined on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algorithms extend and complete other known algorithms for simpler relations and models. The algorithm we pr...

Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. This enables us to arrive at a polynomial time algorithm for deciding ...

This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic bisimulation and can be applied on-the-fly. To support the technique, we introduce a method for detecting confluent transitions in the context of a probabilistic...

in this paper we study the zagreb index in bucket recursive trees containing buckets with variable capacities. this model was introduced by kazemi in 2012. weobtain the mean and variance of the zagreb index andintroduce a martingale based on this quantity.

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.

Infinite groups have been used for cryptography since about twenty years ago. However, it has not been so fruitful as using finite groups. An important reason seems the lack of research on building a solid mathematical foundation for the use of infinite groups in cryptography. As a first step for this line of research, this paper pays attention to a property, the so-called right-invariance, whi...

A complete equational axiomatization of probabilistic bisimulation for nite-state probabilistic processes is presented. It extends Milner's complete axiomatiza