相关论文: Construction of a specification from its singleton…
In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…
We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak{s}_\theta,\mathfrak{p}_\theta,\mathfrak{g}_\theta,\mathfrak{r}_\theta,\mathfrak{t}_\theta$ at uncountable regular…
In this article we give a classification of the binary, simple, $\omega$-categorical structures with SU-rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…
In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong…
We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…
Architecture patterns capture architectural design experience and provide abstract solutions to recurring architectural design problems. They consist of a description of component types and restrict component connection and activation.…
The problem of writing a specification which accurately reflects the intent of the developer has long been recognized as fundamental. We propose a method and a supporting tool to write and check a specification and an implementation using a…
Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categories of discrete and Gaussian probabilistic processes have…
We define a naturality construction for the operations of weak omega-categories, as a meta-operation in a dependent type theory. Our construction has a geometrical motivation as a local tensor product with a directed interval, and behaves…
For a finite relational structure A, let CSP(A) denote the CSP instances whose constraint relations are taken from A. The resulting family of problems CSP(A) has been considered heavily in a variety of computational contexts. In this…
New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the…
Recently, Artemov [4] offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.…