Related papers: Construction Theory, Self-Replication, and the Hal…

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…

Although the conscious state is considered an emergent property of the underlying brain activity and thus somehow resides on brain hardware, there is a non-univocal mapping between both. Given a neural hardware, multiple conscious patterns…

This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…

Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt…

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…

We argue that the halting problem for quantum computers which was first raised by Myers, is by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties that arise in a quantum computer when different…

There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…

This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over…

We introduce and study a learning theory which is roughly automatic, that is, it does not require but a minimum of initial programming, and is based on the potential computational phenomenon of self-reference, (i.e. the potential ability of…

Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…

We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are…

Our representation of the Universe is built with sequences of symbols, numbers, operators, rules and undecidable propositions defining our mathematical truths, represented either by classical, quantum and probabilistic Turing Machines…

For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…

In this paper we consider Kakutani's extension of the Brouwer fixed point theorem within the framework of Bishop's constructive mathematics. Kakutani's fixed point theorem is classically equivalent to Brouwer's fixed point theorem. The…

The halting of universal quantum computers is shown to be incompatible with the constraint of unitarity of the dynamics.

We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…

Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…

In this work, we develop universal quantum computing models that form a family of quantum von Neumann architecture, with modular units of memory, control, CPU, internet, besides input and output. This family contains three generations…

In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…