Fidelity is one of the most widely used quantities in quantum information that measures distance two states through a noisy channel, kind operations. In this paper, we consider model Markov chain (QMC), which transitions are weighted by super-operators to characterize operations and initial state left parametric. A analogy probabilistic computation tree logic, called QCTL, introduced take into ...

The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities, with a well-defined syntax and semantics. Both current approaches, based on Nilsson’s probability structures/logics, and on linear inequalities in order to rea...

A version of Cauchy’s stress theorem is given in which the stress describing the system of forces in a continuous body is represented by a tensor valued measure with weak divergence a vector valued measure. The system of forces is formalized in the notion of an unbounded Cauchy flux generalizing the bounded Cauchy flux by Gurtin & Martins [12]. The main result of the paper says that unbounded C...

A Boolean logic-based evaluation of a database query returns true on match and false on mismatch. Unfortunately, there are many application scenarios where such an evaluation is not possible or does not adequately meet user expectations about vague and uncertain conditions. Consequently, there is a need for incorporating impreciseness and proximity into a logic-based query language. In this wor...

We consider turn-based stochastic games whose winning conditions are conjunctions of satisfaction objectives for long-run average rewards, and address the problem of finding a strategy that almost surely maintains the averages above a given multi-dimensional threshold vector. We show that strategies constructed from Pareto set approximations of expected energy objectives are ε-optimal for the c...

Probabilisticmodel checking is a technique for verifyingwhether amodel such as aMarkov chain satisfies a probabilistic, behavioral property – e.g. ‘‘with probability at least 0.999, a device will be elected leader’’. Such properties are expressible in probabilistic temporal logics, e.g. PCTL, and efficient algorithms exist for checking whether these formulae are true or false on finite-state mo...

In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic ...