Many program-analysis problems can be formulated as graph-reachability problems. Interleaved Dyck language reachability ( InterDyck -reachability) is a fundamental framework to express wide variety of over edge-labeled graphs. The represents an intersection multiple matched-parenthesis languages (i.e., languages). In practice, program analyses typically leverage one achieve context-sensitivity,...

An ideal algorithm for solving a particular problem always finds an optimal solution, finds such a solution for every possible instance, and finds it in polynomial time. When dealing with NP-hard problems, algorithms can only be expected to possess at most two out of these three desirable properties. All algorithms presented in this thesis are exact algorithms, which means that they always find...

Using an orderly algorithm, the Steiner triple systems of order 19 are classified; there are 11,084,874,829 pairwise nonisomorphic such designs. For each design, the order of its automorphism group and the number of Pasch configurations it contains are recorded; 2,591 of the designs are anti-Pasch. There are three main parts of the classification: constructing an initial set of blocks, the seed...

In this paper, we give an algorithm that computes the chromatic number of a graph in O(5.283n) time and polynomial memory.

This paper describes a new exact algorithm PASS for the vértex coloring problem based on the well Keywordsknown DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate Color vértex to color, breaking ties by máximum degree w.r.t. uncolored vértices. Later Sewell introduced a Graph new tiebreaking strategy, which evaluated available colors for each vértex expl...

Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are likely to share many features. In such circumstances, it is natural to leverage similarity among subjects to improve statistical efficiency. The first exact...

In “New Proofs of the structure theorems for Witt Rings”, the first author shows how the standard ring-theoretic results on the Witt ring can be deduced in a quick and elementary way from the fact that the Witt ring of a field is integral and from the specific nature of the explicit annihilating polynomials he provides. We will show in the present article that the same structure results hold fo...

We consider a graph-theoretical formalization of the process of gene assembly in ciliates introduced in Ehrenfeucht et al (2003), where a gene is modeled as a signed graph. The gene assembly, based on three types of operations only, is then modeled as a graph reduction process (to the empty graph). Motivated by the robustness of the gene assembly process, the notions of parallel reduction and p...