Related papers: Unconventional Universal Computation in Babbage's …
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
We consider topological quantum memories for a general class of abelian anyon models defined on spin lattices. These are non-universal for quantum computation when restricting to topological operations alone, such as braiding and fusion.…
The capacity of a channel can usually be characterized as a maximization of certain entropic quantities. From a practical point of view it is of primary interest to not only compute the capacity value, but also to find the corresponding…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
Ising machines are a form of quantum-inspired processing-in-memory computer which has shown great promise for overcoming the limitations of traditional computing paradigms while operating at a fraction of the energy use. The process of…
The Universal Turing Machine (TM) is a model for VonNeumann computers --- general-purpose computers. A human brain can inside-skull-automatically learn a universal TM so that he acts as a general-purpose computer and writes a computer…
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…
Universal induction is a crucial issue in AGI. Its practical applicability can be achieved by the choice of the reference machine or representation of algorithms agreed with the environment. This machine should be updatable for solving…
In this paper, we introduce a new public quantum interactive proof system and the first quantum alternating Turing machine: qAM proof system and qATM, respectively. Both are obtained from their classical counterparts (Arthur-Merlin proof…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
This paper studies the computability of the secrecy capacity of fast-fading wiretap channels from an algorithmic perspective, examining whether it can be computed algorithmically or not. To address this question, the concept of Turing…
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…