An infinite f.g. group G is quasi-finitely axiomatizable (QFA) if there is a first-order sentence j such that G ! j, and if H is a f.g. group such that H ! j, then GGH. The first result is that all Baumslag–Solitar groups of the form ha; d j d"1ad 1⁄4 ai are QFA. A f.g. group G is a prime model if and only if there is a tuple g1; . . . ; gn generating G whose orbit (under the automorphisms of G...

Consider the finite regular language Ln = {w0 | w ∈ {0, 1}, |w| ≤ n}. In [3] it was shown that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum finite automaton (QFA) for it has size 2 . This was based on the fact that the evolution of a QFA is required to be reversible. When arbitrary intermediate measurements are allowed, this intuition bre...

We construct zero-error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded-error probabilistic finite automata (PFAs). Here is a summary of our results: 1. There is a promise problem solvable by an exact two-way QFA in exponential expected time, but not by any bounded-error sublogarithmic space probabilistic Turing machine (PTM). 2. There is a promise problem ...

Multi-letter quantum finite automata (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs [5], and they showed that multi-letter QFAs can precisely accept some regular languages ((a+b)∗b) that are unacceptable by the usual one-way QFAs. In this paper, we continue to deal with multi-letter QFAs, and we mainly focus on two issues: (1) we show that (k+1)-letter Q...

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 modern QFA model involving superoperators that is able to simulate all known QFA and classical finite automaton variants.

The computational model of Quantum Finite Automata has been introduced by multiple authors (e.g. [38, 44]) with some variations in definition. The objective of this thesis is to understand what class of languages can be recognized by these different variations, and how many states are required. We begin by showing that we can use algebraic automata theory to characterize the language recognitio...

We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre’s Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including SL(n, Z) for n ≥ 3. We also give a way of thinking about Property (QFA) by breaking it down into statements about particular classes of trees.

We study the stochastic events induced by MM-qfa’s working on unary alphabets. We give two algorithms for unary MM-qfa’s: the first computes the dimension of the ergodic and transient components of the non halting subspace, while the second tests whether the induced event is d-periodic. These algorithms run in polynomial time whenever the MM-qfa given in input has complex amplitudes with ration...

Abstract: Icing on power transmission lines is a serious threat to the security and stability of the power grid, and it is necessary to establish a forecasting model to make accurate predictions of icing thickness. In order to improve the forecasting accuracy with regard to icing thickness, this paper proposes a combination model based on a wavelet support vector machine (w-SVM) and a quantum f...

We prove that several variants of the quantum finite automaton (QFA) model are strictly superior to their probabilistic counterparts, in terms of both language recognition power and succinctness, in the one-sided unbounded error setting. This is the first case where one-way QFA models have been shown to outperform the corresponding probabilistic automata in both these respects. We give a charac...