Related papers: FIFTH system for general-purpose connectionist com…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Cognitive Architectures are the forefront of the research into developing an artificial cognition. However, they approach the problem from a separated memory and program model of computation. This model of computation poses a fundamental…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
This paper examines conceptual models and their application to computational thinking. Computational thinking is a fundamental skill for everybody, not just for computer scientists. It has been promoted as skills that are as fundamental for…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Computation nowadays is becoming inherently concurrent, either because of characteristics of the hardware (with multicore processors becoming omnipresent) or due to the ubiquitous presence of distributed systems (incarnated in the…
There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…