Related papers: 2-State 3-Symbol Universal Turing Machines Do Not …
We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.
The halting of universal quantum computers is shown to be incompatible with the constraint of unitarity of the dynamics.
The twin primes conjecture is a very old problem. Tacitly it is supposed that the primes it deals with are finite. In the present paper we consider three problems that are not related to finite primes but deal with infinite integers. The…
Although polynomial-time probabilistic Turing machines can utilize uncomputable transition probabilities to recognize uncountably many languages with bounded error when allowed to use logarithmic space, it is known that such "magic coins"…
Two Turing Machines may be able to answer questions about each other that they cannot answer about themselves.
We state a version of the P=?NP problem for infinite time Turing machines. It is observed that P not= NP for this version.
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…
Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass…
We establish a lower bound for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each…
In this paper are discussed some formal properties of quantum devices necessary for implementation of nondeterministic Turing machine.
The notion of quantum Turing machines is a basis of quantum complexity theory. We discuss a general model of multi-tape, multi-head Quantum Turing machines with multi final states that also allow tape heads to stay still.
It is proved that all recursively enumerable sets of natural numbers can be represented by arithmetic formulas (of two kinds) with only 3 quantifiers.
*by a standard (one-tape) Turing machine. It is well-known that the word problem for hyperbolic groups, whence in particular for free groups, can be solved in linear time. However, these algorithms run on machines more complicated than a…
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…
Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
We show that standard nonlocal boxes, also known as Popescu-Rohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to…
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
We show that standard nonlocal boxes, also known as Popescu-Rohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to…
The famous problem of Busy Beavers can be stated as the question on how long a $n$-state Turing machine (using a 2-symbol alphabet or -- in a generalization -- a $m$-symbol alphabet) can run if it is started on the blank tape before it…