Related papers: Synthetic Tait Computability the Hard Way
Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.
We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. (T.1) A basic property of Cantor space $2^{\mathbb{N}}$…
Kant's Critique of Pure Reason, a major contribution to the history of epistemology, proposes a table of categories to elucidate the structure of the a priori principles underlying human judgment. Artificial intelligence (AI) technology,…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular (color) pattern. For k >= 1, k-PATS is a variant of PATS that restricts input patterns to those with at most…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
We give a detailed treatment of the ``bit-model'' of computability and complexity of real functions and subsets of R^n, and argue that this is a good way to formalize many problems of scientific computation. In the introduction we also…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…
We study rational streams (over a field) from a coalgebraic perspective. Exploiting the finality of the set of streams, we present an elementary and uniform proof of the equivalence of four notions of representability of rational streams:…
A new effective method for factorization of a class of nonrational $n\times n$ matrix-functions with \emph{stable partial indices} is proposed. The method is a generalization of the one recently proposed by the authors which was valid for…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
This manuscript explores many convolution (restricted summation) type sequences via certain types of matrix based factorizations that can be used to express their generating functions. The last primary (non-appendix) section of the thesis…
Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
In this paper I argue that infinities in the classical computation theory such as the unsolvability of the Halting Problem can be addressed in the same way as Feynman divergences in Quantum Field Theory, and that meaningful versions of…