相关论文: The G\"odelizing Quantum-Mechanical Automata

In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This…

A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…

We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear…

The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…

We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…

We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict…

We show that a machine, which knows basic logic and arithmetic and basic axioms of knowledge, and which is factive (knows nothing false), can either know that it is factive, or know its own Goedel number, but not both.

Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…

The machinery of quantum mechanics is fully capable of describing a single realistic world. Here we discuss the converse: in spite of appearances, and indeed numerous claims to the contrary, any quantum mechanical model can be mimicked, up…

The purpose of this article is to provide a novel approach and justification of the idea that classical physics and quantum physics can neither function nor even be conceived one without the other - in line with ideas attributed to e.g.…

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…

I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important…

Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for…

We claim that the nonlocality without entanglement revealed quite recently by Bennett {\it et al.} [quant-ph/9804053] should be rather interpreted as {\it Einstein-Podolsky-Rosen paradox without entanglement}. It would be true nonlocality…

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…

We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we…

We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted…

We propose a novel notion of a quantum learning machine for automatically controlling quantum coherence and for developing quantum algorithms. A quantum learning machine can be trained to learn a certain task with no a priori knowledge on…

Three reasonable hypotheses lead to the thesis that physical phenomena can be described and simulated with cellular automata. In this work, we attempt to describe the motion of a particle upon which a constant force is applied, with a…

Many methods for the verification of complex computer systems require the existence of a tractable mathematical abstraction of the system, often in the form of an automaton. In reality, however, such a model is hard to come up with, in…