This paper studies basic properties of probabilistic multirelations which are generalized the semantic domain of probabilistic systems and then provides two probabilistic models of complete IL-semirings using probabilistic multirelations. Also it is shown that these models need not be models of complete idempotent semirings.

We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NP-hard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very eecient techniques for globally complete probabilistic deduction. In ...

We introduce a version of the probabilistic μ-calculus (PMC) built on top of a probabilistic modal logic that allows encoding n-ary inequational conditions on transition probabilities. PMC extends previously studied calculi and we prove that, despite its expressiveness, it enjoys a series of good metaproperties. Firstly, we prove the decidability of satisfiability checking by establishing the s...

We prove the existence of many complete graphs in almost all sufficiently dense partitions obtained by an application of Szemerédi’s Regularity Lemma. More precisely, we consider the number of complete graphs K` on ` vertices in `-partite graphs where each partition class consists of n vertices and there is an ε-regular graph onm edges between any two partition classes. We show that for all β >...

Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NPcomplete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries of its Hessian matrix equal to zero) intersects with a unit hypercube in many-dimensional Euclidean space. This connection suggests the possibility that meth...

The performance of a Content-Based Image Retrieval (CBIR) system presented in the form of Precision-Recall or PrecisionScope graphs offers an incomplete overview of the system under study: the influence of the irrelevant items is obscured. In this paper, we propose a comprehensive and well normalized description of the ranking performance compared to the performance of an Ideal Retrieval System...

Concavely-priced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavely-priced probabilistic timed automata for arbitrary initial states. We prove that these problems are EXPTIME-complete for probabilistic timed automata with two or more clocks and PTIME-com...

Concavely-priced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavely-priced probabilistic timed automata for arbitrary initial states. We prove that these problems are EXPTIME-complete for probabilistic timed automata with two or more clocks and PTIME-com...