Related papers: Relatively acceptable notation
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…
In this paper we shall relate computational complexity to the principle of natural selection. We shall do this by giving a philosophical account of complexity versus universality. It seems sustainable to equate universal systems to complex…
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…
Reproducibility has been consistently identified as an important component of scientific research. Although there is a general consensus on the importance of reproducibility along with the other commonly used 'R' terminology (i.e.,…
The general purpose of a scientific publication is the exchange and spread of knowledge. A publication usually reports a scientific result and tries to convince the reader that it is valid. With an ever-growing number of papers relying on…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
We give a characterization of the strong degrees of categoricity of computable structures greater or equal to $\mathbf 0''$. They are precisely the \emph{treeable} degrees -- the least degrees of paths through computable trees -- that…
The reproduction and replication of research results has become a major issue for a number of scientific disciplines. In computer science and related computational disciplines such as systems biology, the challenges closely revolve around…
This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems…
We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e.…
The paper studies computability-theoretic aspects of topological $T_0$-spaces. We introduce effective versions of the notions of a countable $c$-poset and a (second-countable) topological space with base. Based on this, we prove an…
Architectural imperatives due to the slowing of Moore's Law, the broad acceptance of relaxed semantics and the O(n!) worst case verification complexity of generating sequential histories motivate a new approach to concurrent correctness.…
We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank $\omega_1^{CK}$, the computable infinitary theory is $\aleph_0$-categorical. Millar and Sacks asked whether this…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…