Kolmogorov complexity asks whether a string can be outputted by a Turing Machine (TM) whose description is shorter. Analogously, a real number is considered computable if a Turing machine can generate its decimal expansion. The modern
A symbolic analysis of Archimedes’s periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic po...
Quantum computing allows us to solve some problems much faster than existing classical algorithms. Yet, the quantum computer has been believed to be no more powerful than the most general computing model—the Turing machine. Undecidable problems...
One of Wittgenstein’s most quoted passages from his Remarks on the Philosophy of Psychology concerns Turing’s “machines” and says verbatim: “These machines are humans who calculate. And one might express what he [Turing]...
Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two nu...
An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability&rdq...
We introduce oracle Turing machines with neutrosophic values allowed in the oracle information and then give some results when one is permitted to use neutrosophic sets and logic in relative computation. We also introduce a method to enumerate the el...
Bacterial computing is a known candidate in natural computing, the aim being to construct “bacterial computers” for solving complex problems. In this paper, a new kind of bacterial computing system, named the bacteria and plasmid computin...
Networks of splicing processors (NSP for short) embody a subcategory among the new computational models inspired by natural phenomena with theoretical potential to handle unsolvable problems efficiently. Current literature considers three variants in...
Spiking neural P systems (SNP systems), as computational models abstracted by the biological nervous system, have been a major research topic in biological computing. In conventional SNP systems, the rules in a neuron remain unchanged during the comp...
The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have as...
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not been fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example being the...
The problems associated with the construction of polynomial complexity computer programs require new techniques and approaches from mathematicians. One of such approaches is representing some class of polynomial algorithms as a certain class of speci...
The origin of life has previously been modeled by biological heat engines driven by thermal cycling, caused by suspension in convecting water. Here more complex heat engines are invoked to explain the origin of animals in the thermal gradient above a...
In biological neural networks, neurons transmit chemical signals through synapses, and there are multiple ion channels during transmission. Moreover, synapses are divided into inhibitory synapses and excitatory synapses. The firing mechanism of previ...
As third-generation neural network models, spiking neural P systems (SNP) have distributed parallel computing capabilities with good performance. In recent years, artificial neural networks have received widespread attention due to their powerful inf...
A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable...
It is often of interest to biologists to evaluate whether two populations are alike with respect to a similarity index; assessing the numbers of shared species is one way to do this. In this study, we propose two Turing-type estimators for the probab...
Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. Gödel’s incompleteness argument is explored here to d...
Science is currently becoming aware of the challenges in the understanding of the very root mechanisms of massively parallel computations that are observed in literally all scientific disciplines, ranging from cosmology to physics, chemistry, biochem...
The AKS algorithm is an important breakthrough in showing that primality testing of an integer can be done in polynomial time. In this paper, we study the optimization of its runtime. Namely, given a finite cardinality set of alphabets of a determini...
Genetic programming (GP) has a long-standing tradition in the evolution of computer programs, predominantly utilizing tree and linear paradigms, each with distinct advantages and limitations. Despite the rapid growth of the GP field, there have been...
Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show th...
Spiking neural P systems (SN P systems for short) realize the high abstraction and simulation of the working mechanism of the human brain, and adopts spikes for information encoding and processing, which are regarded as one of the third-generation ne...
With the advent of IoT and Cloud computing service technology, the size of user data to be managed and file data to be transmitted has been significantly increased. To protect users’ personal information, it is necessary to encrypt it in secure...
The term artificial intelligence has existed for several decades, but its real boom has been recorded in the last five years due to the development of powerful computing capabilities and advances in the field of algorithms. Historically, artificial i...
Zero-shot generalization to out-of-distribution (OOD) teammates and opponents in multi-agent systems (MASs) remains a fundamental challenge for general-purpose AI, especially in open-ended interaction scenarios. Existing multi-agent reinforcement lea...