Related papers: Finite automata models of quantized systems: conce…

Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…

We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…

Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive…

The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the…

The theory of finite automata applies to the study on relations of multiple zeta values.

To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between…

We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a…

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…

One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.

In the literature, there exist several quantum finite automata (QFA) models with both quantum and classical states. These models are of particular interest,as they show praiseworthy advantages over the fully quantum models in some…

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…

This paper is a continuation of a previous study on the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We investigate conditions assuring that, given a language recognized by such a device…

This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…

Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…

This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…

Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…

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…

Herein we survey the main results concerning quantum automata and machines with classical control. These machines were originally proposed by Sernadas et al in [37], during the FCT QuantLog project. First, we focus on the expressivity of…

Quantum finite automata, as well as quantum pushdown automata (QPA) were first introduced by C. Moore and J. P. Crutchfield. In this paper we introduce the notion of QPA in a non-equivalent way, including unitarity criteria, by using the…