Two-way Nanoscale automata (original) (raw)

Acta Informatica

one-way quantum finite automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by one-way quantum finite automata is a proper subset of regular languages. In this paper, we replace the tape head of one-way quantum finite automata with DNA double strand and name the model Watson-Crick quantum finite automata. The noninjective complementarity relation of Watson-Crick automata introduces non-determinism in the quantum model. We show that this introduction of non-determinism increases the computational power of one-way Quantum finite automata significantly. We establish that Watson-Crick quantum finite automata can accept all regular languages and that it also accepts some languages which are not accepted by any multi-head deterministic finite automata. Exploiting the superposition property of quantum finite automata we show that Watson-Crick quantum finite automata accept the language L={ww |w∈ , * }.

Multi-head Watson-Crick quantum finite automata

ArXiv, 2020

Watson-Crick quantum finite automata were introduced by Ganguly this http URL. by combining properties of DNA and Quantum automata. In this paper we introduce a multi-head version of the above automaton. We further show that the multi-head variant is computationally more powerful than one-way multi-head reversible finite automata. In fact we also show that the multi-head variant accepts a language which is not accepted by any one-way multi-head deterministic finite automata.

2-tape 1-way Quantum Finite State Automata

ArXiv, 2016

1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape 1-way quantum finite state automaton (2T1QFA(2))which is a modified version of 1-way 2-head quantum finite state automaton(1QFA(2)). In this paper, we replace the single tape of 1-way 2-head quantum finite state automaton with two tapes. The content of the second tape is determined using a relation defined on input alphabet. The main claims of this paper are as follows: (1)We establish that 2-tape 1-way quantum finite state automaton(2T1QFA(2)) can accept all regular languages (2)A language which cannot be accepted by any multi-head deterministic finite automaton can be accepted by 2-tape 1-way quantum finite state automaton(2T1QFA(2)) .(3) Exploiting the superposition property of quantum automata we show that 2-tape 1-way quantum finite state au...

1Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations

1998

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFA can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata.

Two-way Quantum One-counter Automata

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.

Two-way Nanoscale automata (original) (raw)

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