Evaluation of twig queries over probabilistic XML is investigated. Projection is allowed and, in particular, a query may be Boolean. It is shown that for a well-known model of probabilistic XML, the evaluation of twigs with projection is tractable under data complexity (whereas in other probabilistic data models, projection is intractable). Under queryand-data complexity, the problem becomes in...

The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC ) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect ...

We study a probabilistic optimization model for MIN SPANNING TREE, where any vertex vi of the input-graph G(V, E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Supposing that when this “real” instance G′ becomes known, a decision maker might have no time to perform computation from scratch, we assume that a spanning tree T , called anticipator...

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

We study the complexity of some new probabilistic variant of the problem Quantified Satisfiability(QSAT). Let a sentence ∃v1∀v2 . . . ∃vn−1∀vnφ be given. In classical game associated with the QSAT problem, the players ∃ and ∀ alternately chose Boolean values of the variables v1, . . . , vn. In our game one (or both) players can instead determine the probability that vi is true. We call such pla...

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...

Nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. In this work we introduce this concept in an $S$-poset, aposet with an action of a posemigroup $S$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $S$-net. Using $S$-nets and itsconvergency we...

This paper extends the concept of probabilistic completeness defined for the motion planners in the absence of noise, to the concept of “probabilistic completeness under uncertainty” for the motion planners that perform planning in the presence of uncertainty. According to the proposed definition, an approach is proposed to verify the probabilistic completeness under uncertainty. Finally, it is...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...