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Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs…
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
The physical limits to computation have been under active scrutiny over the past decade or two, as theoretical investigations of the possible impact of quantum mechanical processes on computing have begun to make contact with realizable…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's…
Alan Turing's pioneering work on computability, and his ideas on morphological computing support Andrew Hodges' view of Turing as a natural philosopher. Turing's natural philosophy differs importantly from Galileo's view that the book of…
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…
Church's hypothesis and Godel's theorem may provide constraints on mental processes.As a relief quantum entanglement may lead to a definite proposal as regards the nature of reality and how much of it we are able to know and how do we know…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are…
One of the main uses of computers is to do statistical analysis of data. But, so far, the theory of statistics, and its noble mother, Probability theory, were all discovered and developed by lowly humans. No more! Computers can also develop…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…