Graphical Interval Logic (GIL) is a temporal logic in which all reasoning is done by means of diagram-matic formull. It is a discrete linear-time modal logic in which the basic temporal modality is the interval. Future Interval Logic (FIL) provides the logical foundation for GIL. In this paper we present an automata-theoretic decision procedure for FIL with complexity DTIME(2 O(n k)), where n i...

In this paper we treat a resource allocation model defined on an infinite interval. We show that the solution of the corresponding problem with finite horizon cannot be extended to a solution of the infinite horizon problem, since the resource allocation problem in the unmodified setting does not have a solution on an unbounded interval. To change this situation we bring an additional state con...

We discuss control systems defined on an infinite horizon, where typically all the associated costs become unbounded as the time grows indefinitely. It is proved, under certain lower semicontinuity and controllability assumptions, that a linear time function can be subtracted from the cost, resulting in a modified cost, which is bounded on the infinite time interval. The cost evaluated over one...

New quadrature formulas (QFs) for evaluating the singular integral (SI) of Cauchy type with unbounded weight function on the edges is constructed. The construction of the QFs is based on the modification of discrete vortices method (MMDV) and linear spline interpolation over the finite interval [−1,1]. It is proved that the constructed QFs converge for any singular point x not coinciding with t...

Robust counterpart optimization techniques are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geome...