OF THE DISSERTATION On Generation of Cut Conjunctions, Minimal k-Connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices by Konrad Borys Dissertation Director: Professor Endre Boros We consider the following problems: • Cut conjunctions in graphs: given an undirected graphG = (V,E) and a collection of vertex pairs B ⊆ V × V generate all minimal edge sets X ⊆ E such tha...

The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as phenomenological modification Heisenberg's uncertainty relation. We show that this equivalent to cut-off in the space conjugate position representation, i.e. wave numbers, which does not necessarily correspond momentum space. This result generalized several dimensions and noncommuta...

Let an edge cut partition the vertex set of the n-cube into k subsets A1, ..., Ak with ||Ai| − |Aj || ≤ 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n, k → ∞ and also as n → ∞ and k is a constant of the form k = 2a ± 2b with a ≥ b ≥ 0.

Nowadays, embedded systems are commonly used. Embedded System’s complexity can vary from low, e.g., a single micro-controller chip, to very high, e.g., robots. In order to assure the safety of the embedded system to living beings and / or the environment, the systems should be examined and analyzed. It is extremely difficult to analyze safety issues in complex embedded systems using only the st...

Embedded systems, which are safety critical, are frequently analyzed to find out whether they follow the safety standards and to improve their safety. Fault tree analyses enable the safety analysts to find possible causes of a system’s failure or unsafe behavior. From a fault tree, minimal cut sets are computed giving unique combinations of basic events that cause such a failure. Using minimal ...

This paper proposes an efficient cut set approach to enumerate the subsets cut groups (SCG) from apriori knowledge of minimal cutsets of a network. These SCG block a given amount of flow through the network despite the network being (s, t) connected and are being used to evaluate capacity related reliability (CRR) by employing any sum of disjoint product approach. For each minimal cutset and a ...