Algebraic and Logical Characterizations of Quantum Büchi Automata

HAN Zhao-wei

doi:10.3969/j.issn.0372-2112.2013.06.009

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Algebraic and Logical Characterizations of Quantum Büchi Automata

更新时间：2025-07-16

- Algebraic and Logical Characterizations of Quantum Büchi Automata
- Acta Electronica Sinica Vol. 41, Issue 6, Pages: 1093-1100(2013)
- 作者机构：
  
  1. 陕西师范大学数学与信息科学学院,陕西,西安,710062
  2. 陕西师范大学数学与信息科学学院,陕西,西安,710062
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11271237);National Natural Science Foundation of China Tianyuan Fund For Mathematics (No.11226266);Research Fund for Shaanxi Normal University (No.999553)
- DOI：10.3969/j.issn.0372-2112.2013.06.009
  CLC： TP301.1O153.1
- Published：2013
- 稿件说明：
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HAN Zhao-wei. Algebraic and Logical Characterizations of Quantum Büchi Automata[J]. Acta Electronica Sinica, 2013, 41(6): 1093-1100.
DOI：

HAN Zhao-wei. Algebraic and Logical Characterizations of Quantum Büchi Automata[J]. Acta Electronica Sinica, 2013, 41(6): 1093-1100. DOI： 10.3969/j.issn.0372-2112.2013.06.009.

摘要

提出量子Bchi自动机(简记为LVBA)的概念

利用量子状态构造方法证明了一般LVBA与状态转移为经典函数的LVSBA间的相互等价性

籍此研究了量子无穷正则语言的代数刻画、层次刻画和Bchi刻画以及对于正则运算的封闭性;通过引入单体二阶量子逻辑(简记为LVMSO)的概念

给出量子Bchi自动机所识别无穷语言的单体二阶逻辑描述

深化和推广了量子逻辑意义下的Bchi基本定理.

Abstract

The notion of quantum Bchi automaton (LVBA for short)is introduced

by means of quantum state construction

the equivalence of an LVBA and an LVSBA with crisp transition function is proved

based on this

the algebraic and level characterizations and also the Bchi characterization of quantum infinite regular languages are investigated

and also the closed properties of those quantum infinite regular languages under some regular operations are dealt with.By providing the concept of monadic second-order quantum logic(LVMSO in short)

the monadic second-order logic characterizations of infinite regular languages recognized by quantum Bchi automata are presented

which deepen and generalize the fundamental Bchi theorem to quantum setting.

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