Related papers: The Epistemic Landscape: a Computability Perspecti…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
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…
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…
A common concern in experimental research is the auditability and reproducibility of experiments. Experiments are usually designed, provisioned, managed, and analyzed by diverse teams of specialists (e.g., researchers, technicians and…
Computability theory is traditionally conceived as the theoretical basis of informatics. Nevertheless, numerous proposals transcend computability theory, in particular by emphasizing interaction of modules, or components, parts,…
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
Possible for science itself, conceptually, to have and will understand differently, let alone science also seen as technology, such as computer science. After all, science and technology are viewpoints diverse by either individual,…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From…
Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term "the tip…
It is possible to enumerate all computer programs. In particular, for every partial computable function, there is a shortest program which computes that function. f-MIN is the set of indices for shortest programs. In 1972, Meyer showed that…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
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…
This thesis presents a series of theoretical results and practical realisations about the theory of computation in distributive categories. Distributive categories have been proposed as a foundational tool for Computer Science in the last…
Computer programs are part of our daily life, we use them, we provide them with data, they support our decisions, they help us remember, they control machines, etc. Programs are made by people, but in most cases we are not their authors, so…
Those seeking to reproduce a computational experiment often need to manually look at the code to see how to build necessary libraries, configure parameters, find data, and invoke the experiment; it is not automatic. Automatic…
A problem is a multivalued function from a set of \emph{instances} to a set of \emph{solutions}. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness…
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…
What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…