Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrating theory reasoning. However, for numerous applications from program analysis and verification, the ground fragment is insufficient, as proof obligations often include quantifiers. A well known approach for quantifier reasoning uses a matching algorithm that works against an E-graph to ...

The existence of an integral flow polynomial that counts nowhere-zero k-flows on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes. The same holds for flows on signed graphs. We develop these theories, as well as the related counting theory of nowhere-zero flows on a signed graph with values in an abelian group of odd order. Our results are of two kinds: polyn...

Quantitative analysis of website has been applied widely in the structure design of the websites. Web metrics such as Web graph theory, Web page significance, Webpage Search and Retrieval and Usage Characterization have been researched for many years, aiming at providing good guidance for the structure design of website. But all the metrics need to be practiced to promote the theories themselve...

Abstract We introduce a persistent Hochschild homology framework for directed graphs. groups of (path algebras of) graphs vanish in degree $$i\ge 2$$ i ≥ 2 . To extend them to higher degrees, we the notion connectivity digraphs , and analyse two main ex...

Abstract—The solution of non linear problems are based on very well grounded mathematical theories. This document proposes a Newton step graph-based model for convex non linear separable problems (NLP) with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLSP model will grow in a non linear manner. Furthermore, the constraints ha...

We give the first (ZFC) dividing line in Keisler’s order among the unstable theories, specifically among the simple unstable theories. That is, for any infinite cardinal λ for which there is μ < λ ≤ 2, we construct a regular ultrafilter D on λ such that (i) for any model M of a stable theory or of the random graph, M/D is λ-saturated but (ii) if Th(N) is not simple or not low then N/D is not λ-...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...

We introduce inductive limits of compact quantum groups and their unitary representation theories. Those give a more explicit representation-theoretic meaning to our previous study quantization characters central probability measures in the asymptotic theory. also tensor product representations infinite-dimensional group. As by-product, we an interpretation certain transformations that play imp...

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...