Related papers: Bit Copying - The Ultimate Computational Simplicit…
By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…
Basic experimental findings about human working memory can be described by an algebra built on high-dimensional binary states, representing information items, and two operations: multiplication for binding and addition for bundling. In…
In a previous paper, we provided a formal definition for the concept of computational irreducibility (CIR), i.e. the fact for a function f from N to N that it is impossible to compute f(n) without following approximately the same path than…
A common technique for checking properties of complex state machines is to build a finite abstraction then check the property on the abstract system -- where a passing check on the abstract system is only transferred to the original system…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
Turing machines and register machines have been used for decades in theoretical computer science as abstract models of computation. Also the $\lambda$-calculus has played a central role in this domain as it allows to focus on the notion of…
This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.
In the present work we will present and analyze some basic processes at the local and global level in linguistic derivations that seem to go beyond the limits of Markovian or Turing-like computation, and require, in our opinion, a quantum…
The ability to express a program as a hierarchical composition of parts is an essential tool in managing the complexity of software and a key abstraction this provides is to separate the representation of data from the computation. Many…
In existing systems, the off-chip memory interface allows the memory controller to perform only read or write operations. Therefore, to perform any operation, the processor must first read the source data and then write the result back to…
In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…
In classical computation, a "write-only memory" (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented…
Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register…
This work exposes which mechanisms and procesess in the Nature of evolution compute a function not computable by Turing machine. The computer with intelligence that is not higher than one bacteria population could have, but with efficency…
We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum…
We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. In terms of spin components, for spin-1/2 particle spin…
The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here…
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and…
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…
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…