Two-way Nanoscale automata (original) (raw)

Eprint Arxiv Cs 0110005, 2001

After the first treatments of quantum finite state automata by Moore and Crutchfield and by Kondacs and Watrous, a number of papers study the power of quantum finite state automata and their variants. This paper introduces a model of two-way quantum one-counter automata (2Q1CAs), combining the model of two-way quantum finite state automata (2QFAs) by Kondacs and Watrous and the model of one-way quantum one-counter automata (1Q1CAs) by Kravtsev. We give the definition of 2Q1CAs with well-formedness conditions. It is proved that 2Q1CAs are at least as powerful as classical two-way deterministic one-counter automata (2D1CAs), that is, every language L recognizable by 2D1CAs is recognized by 2Q1CAs with no error. It is also shown that several non-context-free languages including {a n b n 2 | n ≥ 1} and {a n b 2 n | n ≥ 1} are recognizable by 2Q1CAs with bounded error.

Efficient probability amplification in two-way quantum finite automata

Theoretical Computer Science, 2009

In classical computation, one only needs to sequence O(log 1) identical copies of a given probabilistic automaton with one-sided error p < 1 to run on the same input in order to obtain a two-way machine with error bound. For two-way quantum finite automata (2qfa's), this straightforward approach does not yield efficient results; the number of machine copies required to reduce the error to can be as high as (1) 2. In their celebrated proof that 2qfa's can recognize the non-regular language L = {a n b n | n > 0}, Kondacs and Watrous use a different probability amplification method, which yields machines with O((1) 2) states, and with runtime O(1 |w|), where w is the input string. In this paper, we examine significantly more efficient techniques of probability amplification. One of our methods produces machines which decide L in O(|w|) time (i.e. the running time does not depend on the error bound) and which have O((1) 2 c) states for any given constant c > 1. Other methods, yielding machines whose state complexities are polylogarithmic in 1 , including one which halts in o(log(1)|w|) time, are also presented.

A Study on the Quantum Cellular Automata (Qca)-An Advanced Nanotechnology

2016

Quantum cellular automata (QCA) is an advanced nanotechnology that attempts to create general computational at the nano scale by controlling the position of single electrons. QCA technology has large potential in terms of high space density and power dissipation with the development of the faster computer with smaller size & low power consumption. The logic design of ALU, an important constituent part of CPU, is described in this paper. A design constructing 4-bit Arithmetic Logic Unit (ALU) based on the QCA (Quantum-Dot Cellular Automata) is presented. The proposed 4-bit Arithmetic Logic Unit is simulated using the QCA Designer tool and experiment result shows that the arithmetic & logical function of the designed circuit is correct. Our aim is to provide evidence that QCA has potential applications in future computers provided that the underlying technology is made feasible.

Quantum automata and quantum computing

2002

Quantum finite automata were introduced by C. Moore and J. P. Crutchfield in [MC 97] and by A. Kondacs and J. Watrous in [KW 97]. This notion is not a generalization of the deterministic finite automata, but rather a generalization of deterministic reversible (permutation) automata. In [AF 98] A. Ambainis and R. Freivalds raised the question what kind of probabilistic automata can be viewed as a special case of quantum finite automata. To answer that question and study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We give the necessary condition for a language to be recognized by PRA. Vie find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. In these thesis we regard quantum automata, probabilistic reversible and deterministic reversible automata as reversible automata. At l...

State Complexity of Reversible Watson-Crick Automata

ArXiv, 2020

Reversible Watson-Crick automata introduced by Chatterjee this http URL. is a reversible variant of an Watson-Crick automata. It has already been shown that the addition of DNA properties to reversible automata significantly increases the computational power of the model. In this paper, we analyze the state complexity of Reversible Watson-Crick automata with respect to non-deterministic finite automata. We show that Reversible Watson-Crick automata in spite of being reversible in nature enjoy state complexity advantage over non deterministic finite automata. The result is interesting because conversion from non deterministic to deterministic automata results in exponential blow up of the number of states and classically increase in number of heads of the automata cannot compensate for non-determinism in deterministic and reversible models.

Computational Power of Quantum and Probabilistic Automata

acadlib.lv

The thesis assembles research on two models of automata-probabilistic reversible (PRA) that appear very similar to 1-way quantum finite automata (1-QFA) and quantum one-way one counter automata (Q1CA), that is the most restricted model of non-finite space quantum automata. The objective of the research is to describe classes of languages recognizable by these models and compare related quantum and probabilistic automata. We propose the model of probabilistic reversible automata. We study both one-way PRA with classical (1-C-PRA) and decide and halt (1-DH-PRA) acceptance. We show recognition of general class of languages L n = a * 1 a * 2. .. a * n with probability 1 − ε. We show whether the classes of languages they recognize are closed under boolean operations and describe general class of languages not recognizable by these automata in terms of "forbidden constructions" for the minimal deterministic automaton of the language. We also consider "weak" reversibility as equivalent definition for 1-way automata and show the difference from ordinary reversibility in 1.5-way case. We propose the general notion of quantum one-way one counter automata(Q1CA). We describe well-formedness conditions for the Q1CA that ensure unitarity of its evolution. A special kind of Q1CA, called simple, that satisfies the well-formedness conditions is introduced. We show recognition of several non context free languages by Q1CA. We show that there is a language that can be recognized by quantum one-way one counter automaton, but not by the probabilistic one counter automaton. 10. Quantum Computation and Learning. 1st International Workshop. Riga, Latvia, September 11-13, 1999. Presentation "Quantum One Counter Automata". I thank my co-authors Richard Bonner, Rūsiņš Freivalds, Marats Golovkins, Vasilijs Kravcevs, who significantly contributed to this research. I thank Arnolds Ķ ikusts and Andrey Dubrovski for useful discussions. Especially I thank my supervisor Prof. Rūsiņš Freivalds, whose ideas, support and positive attitude was one of the key factors for me to pursue and complete the research. CONTENTS 3.6.2 1.5-way Probabilistic Reversible Automata. .. .. .. 4 Quantum one way 1 counter automata 4.1 Definition of Q1CA .

Quantum Finite Automata: A Modern Introduction

Lecture Notes in Computer Science, 2014

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. Some parts of the material are based on the lectures given by the second author during his visits to Kazan Federal University, Ural Federal University, and Bogaziçi University in 2013. Yakaryılmaz was partially supported by CAPES, ERC Advanced Grant MQC, and FP7 FET project QALGO.

Succinctness of two-way probabilistic and quantum finite automata

Discrete Mathematics & Theoretical Computer Science, 2010

We introduce a new model of two-way finite automaton, which is endowed with the capability of resetting the position of the tape head to the left end of the tape in a single move during the computation. Several variants of this model are examined, with the following results: The weakest known model of computation where quantum computers recognize more languages with bounded error than their classical counterparts is identified. We prove that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions (1PFAs and 1QFAs), and two-way nondeterministic finite automata (2NFAs). For this purpose, we demonstrate several infinite families of regular languages which can be recognized with some fixed probability greater than 1 2 by just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with a constant number of states, whereas the sizes of the corresponding 1PFAs, 1QFAs and 2NFAs grow without bound. We also show that 2QFAs with mixed states can support highly efficient probability amplification.

1-Way Multihead Quantum Finite State Automata

Applied Mathematics, 2016

1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has been shown by Moore and Crutchfield as well as Konadacs and Watrous that 1QFA can't accept all regular language. In this paper, we show different language recognizing capabilities of our model 1-way multihead QFAs. New results presented in this paper are the following ones: 1) We show that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages. 2) A language which can't be accepted by 1-way deterministic 2-head finite state automaton (1DFA((2)) can be accepted by 1QFA(2) with bounded error. 3) 1QFA(2) is more powerful than 1-way reversible 2-head finite state automaton (1RMFA(2)) with respect to recognition of language.

One-way quantum finite automata together with classical states

Arxiv preprint arXiv: …

One-way quantum finite automata (1QFA) proposed by Moore and Crutchfield and by Kondacs and Watrous accept only subsets of regular languages with bounded error. In this paper, we develop a new computing model of 1QFA, namely, one-way quantum finite automata ...