Related papers: A Programming Language Oriented Approach to Comput…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
Classical models of computation have been successful in capturing the very essence of individual computing devices. Although they are useful to understand computability power and limitations in the small, such models are not suitable to…
The words ``Programming is the second literacy'' were coined more than 40 years ago but never came to life. This paper is one in the series of papers aimed at the analysis of mathematical requirements for a merge of school mathematics with…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
Automatic Programming is one of the most important areas of computer science research today. Hardware speed and capability have increased exponentially, but the software is years behind. The demand for software has also increased…
Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the…
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the…
Rapid technological progress in computer sciences finds solutions and at the same time creates ever more complex requirements. Due to an evolving complexity todays programming languages provide powerful frameworks which offer standard…
In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished…
Computational approach to politeness is the task of automatically predicting and generating politeness in text. This is a pivotal task for conversational analysis, given the ubiquity and challenges of politeness in interactions. The…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…
To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more…
Clausal Language (CL) is a declarative programming and verifying system used in our teaching of computer science. CL is an implementation of, what we call, $\mathit{PR}{+}I\Sigma_1$ paradigm (primitive recursive functions with…
The recent progress of artificial intelligence(AI) has shown great potentials for alleviating human burden in various complex tasks. From the view of software engineering, AI techniques can be seen in many fundamental aspects of…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…