Related papers: Three computational models and its equivalence
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
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…
The increase of existing computational capabilities has made simulation emerge as a third discipline of Science, lying midway between experimental and purely theoretical branches [1, 2]. Simulation enables the evaluation of quantities which…
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 replicability crisis is a major issue across nearly all areas of empirical science, calling for the formal study of replicability in statistics. Motivated in this context, [Impagliazzo, Lei, Pitassi, and Sorrell STOC 2022] introduced…
Generalising slightly the notions of a strict computability model and of a simulation between them, which were elaborated by Longley and Normann, we define canonical computability models over categories and appropriate Set-valued functors…
The educability model is a computational model that has been recently proposed to describe the cognitive capability that makes humans unique among existing biological species on Earth in being able to create advanced civilizations.…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
This paper looks at Turing's postulations about Artificial Intelligence in his paper 'Computing Machinery and Intelligence', published in 1950. It notes how accurate they were and how relevant they still are today. This paper notes the…
Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
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…
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
The term `hypermachine' denotes any data processing device (theoretical or that can be implemented) capable of carrying out tasks that cannot be performed by a Turing machine. We present a possible quantum algorithm for a classically…
What would you teach if you had only one course to help students grasp the essence of computation and perhaps inspire a few of them to make computing a subject of further study? Assume they have the standard college prep background. This…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
Selman's Theorem in classical Computability Theory gives a characterization of the enumeration reducibility for arbitrary sets in terms of the enumeration reducibility on the total sets: $A \le_e B \iff \forall X [X \equiv_{e} X \oplus…
In 1957, Lacombe initiated a systematic study of the different possible notions of "computable topological spaces". However, he interrupted this line of research, settling for the idea that "computably open sets should be computable unions…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…