On the Structure of Finite Automata of Which M Is an(Weak)Inverse with Delay τ

In this paper,we first give a method that for any inverse finite automaton M' withdelay τ,all inver tible finite automata with delay τ,of which M' is an inverse with delayτ,can be constructed;and a universal nondeterministic finite automaton,for all finiteautomata of which M' is an inverse with delay τ,can also be constructed.We then give amethod that for any weak inverse finite automaton M' with delay τ,all weaklyinvertible finite automata with delay τ of which M' is a weak inverse with delay,can beconstructed;and a universal nondeterministic finite automaton,for all finiteautomata of which M' is a weak inverse with delay τ,can also be constructed.     

弱可逆拟(r,r)阶存贮线性有限自动机的分解

通过对延迟r步弱可逆拟(r,r)阶存贮线性有限自动机输出权的研究,得出对延迟r步弱可逆拟(r,r)阶存贮线性有限自动机的任意一个状态,它的长r的输出权都是1;任何一个n元拟(r,r)阶存贮线性有限自动机M延迟r步弱可逆的充分必要条件是M都可以分解为一个延迟0步弱可逆有限自动机M0和一个延迟r步弱可逆拟(0,r)阶存贮线性有限自动机M1。     

Structure of weakly invertible semi-input-memory finite automata with delay 2

Semi-input-memory finite automata,a kind of finite automata introduced by the author of this paper for studying error propagation,are a generalization of input-memory finite automata by appending an autonomous finite automaton component.This paper gives a characterization on the structure of weakly invertible semi-input-memory finite automata with delay 2 in which input alphabets and output alphabets have two elements and autonomous finite automata are cyclic.For the structure of feedforward inverse finite automata with delay 2,Zhu first gave a characterization;from a result on mutual invertibility of finite automata,the result mentioned above also leads to a different characterization on the structure of feedforward result mentioned above also leads to a different characterization on the structure of feedforward inverse finite automata with delay 2.     

环上线性有限自动机的可逆性的一些结果

本文证明了有单位元的有限交换环R上任何延迟t步(弱)可逆线性有限自动机皆有延迟t步线性(弱)逆的充分必要条件是环R满足条件: x(Ax=0→bx=0)→y(b=yA)我们还证明了对任何有单有限交换环R,R上输入、输出维数相同的延迟t步(弱)可逆线性有限自动机具有延迟t步线性(弱)逆.     

关于二元延迟3步前馈逆有限自动机的结构

前馈逆有限自动机的结构是有限自动机可逆性理论中的基本问题.对延迟步数≥3的前馈逆结构的刻划,则是一个长期的未解决问题.研究了二元延迟3步前馈逆有限自动机的结构.对于自治有限自动机M_a的状态图为圈的二元延迟3步弱可逆半输入存储有限自动机C(M_af ),给出了其长3极小输出权分别为1,2,8三种情形下结构的一种刻画.由于C(M_af )延迟3步弱可逆当且仅当它是延迟3步弱逆,因此,得到了二元延迟3步前馈逆有限自动机结构的一种部分刻画.     

Structure of Weakly Invertible Semi-Input-Memory Finite Automata with Delay 1

Semi-input-memory finite automata,a kind of finite automata introduced by the first author of this paper for studying error propagation ,are a generalization of inputmemory finite automata ,by appending an autonomous finite automation component .In this paper,we give a characterization of the structure of weakly invertible semi-input-memory finite automata with delay 1,in which the state graph of each autonomous finite automation is cycle,From a result on mutual invertibility of finite automata obtained by th authors recently,it leads to a characerization of the structure of feedfoward inverse finite automata with delay 1.     

拟(h,k)存贮有限自动机的可逆性

主要研究拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱可逆性,以及它的弱逆,得到了拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱可逆的充分必要条件,并且通过所得结果可以比较简便地构造出延迟k步与k+1步弱可逆拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱逆.     

线性有限自动机输入输出集的性质

证明了两个线性有限自动机化合而得到的自动机具有输入输出均匀的性质,建立了由两个延迟1步弱可逆线性有限自动化合后得到的自动机的输入集个数与化合前自动机输入集个数的等式关系。     

关于弱可逆有限自动机延迟步数分解的两个结果

本文证明存在(任意元)延迟2步弱可逆有限自动机不等价于任何两个延迟1步弱可逆有限自动机的化合的任何子自动机。因而说明了不是对所有的弱可逆有限自动机,延迟步数都是可分解的,但对所有状态的延迟步数均为2的二元延迟2步弱可逆有限自动机,则分解是可行的。     

Input-trees of finite automata and application to cryptanalysis

In this paper,Weights of output set and of input set for finite automata are discussed.For a weakly invertible finite automaton,we prove that for states with minimal output weight,the distruibution of input sets is uniform.Then for a kind of compound finite automata,we give weights of output set and of input set explicitly,and a characterization of their input-trees.For finite automaton public key cryptosystems,of which automata in public keys belong to such a kind of compound finite automata,we evaluate search amounts of exhaust search algorithms in average case and in worse case for both encryption and signature,and success ful probabilities of stochastic search algorithms for both encryption and signature.In addition,a result on mutual invertibility of inite automata is also given.     

拟（h,k）存贮有限自动机的可逆性

主要研究拟（h,k）阶存贮有限自动机的延迟k步与k＋1步弱可逆性,以及它的弱逆,得到了拟（h,k）阶存贮有限自动机的延迟k步与k＋1步弱可逆的充分必要条件,并且通过所得结果可以比较简便地构造出延迟k步与k＋1步弱可逆拟（h,k）阶存贮有限自动机的延迟k步与k＋1步弱逆。     

弱可逆线性有限自动机的一种分解

讨论有限自动机的分解有助于分析弱可逆有限自动机的结构和求解弱逆.首先证明了弱同构的弱可逆有限自动机具有相似的分解形式;接着考虑了一类特殊的弱可逆线性有限自动机的分解,从状态输出权的角度刻画了该分解存在的一个充分条件;然后把这种分解形式推广到了一般的弱可逆线性有限自动机上,即:延迟τ步弱可逆线性有限自动机分解成延迟0步弱可逆有限自动机和一种特殊的有限自动机MD,并得到了分解存在的充要条件;最后,用输出序列的代数性质来刻画其中的充分条件,并把它转化成了一个矩阵的秩的计算.这种分解形式并不局限于n元弱可逆有限自动机,而且分解条件也比较简单,仅与输出序列的性质有关.     

On the Structure of (Weak) Inverses of an (Weakly) Invertible Finite Automaton

In this paper, we first give a method by which, for any weakly invertible finite automatonM with delay τ, the set of all weak inverse finite automata of M with delay τ can beconstructed. We then give a method by which, for any invertible one, all its inverses with delayτ can also be constructed.     

Prediction and Welfare in Ad Auctions

We prove that semigroups generated by reversible two-state Mealy automata have remarkable growth properties: they are either finite or free. We give an effective procedure to decide finiteness or freeness of such semigroups when the generating automaton is also invertible.     

有限自动机定义函数的线性本原圈积分解

本文讨论有限自动机显表出定义函数ｆ的线性本原圈积分解问题。在该圈积分解之下,函数ｆ被表成线性外函数因子ｆＬ与线性本原内涵数因子ｆＮ的圈积,这里函数ｆＬ定义了一个线性弱可逆有限自动机ＭｆＬ,而函数ｆＮ定义了一个非线性有限自动机ＭｆＮ且其不能再分解成一非平凡的线性外函数与一非线性内函数的圈积。本文证明了一函数ｆ的任两线性本原内因子互为对方的线性本原内因子,从而证明了函数ｆ的线性本原圈积分解的唯一性。本     

Cooperating systems of four-dimensional finite automata

M. Blum and C. Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern processing in 1967, and investigated their pattern recognition abilities. Since then, many researchers in this field have investigated many properties of automata on a two- or three-dimensional tape. However, the question of whether processing four-dimensional digital patterns is much more difficult than processing two- or three-dimensional ones is of great interest from both theoretical and practical standpoints. Thus, the study of four-dimensional automata as a computational model of four-dimensional pattern processing has been meaningful. This article introduces a cooperating system of four-dimensional finite automata as one model of four-dimensional automata. A cooperating system of four-dimensional finite automata consists of a finite number of four-dimensional finite automata and a four-dimensional input tape, where these finite automata work independently (in parallel). The finite automata whose input heads scan the same cell of the input tape can communicate with each other, i.e., every finite automaton is allowed to know the internal states of other finite automata on the cell it is scanning at the moment. In this article we mainly investigate the accepting powers of a cooperating system of seven-way four-dimensional finite automata. The seven-way four-dimensional finite automaton is a four-dimensional finite automaton whose input head can move east, west, south, north, up, down, or in the future, but not in the past, on a four-dimensional input tape.     

The cartesian composition of automata

There are several known ways to define a product automaton on the cartesian product of the state sets of two given automata. This paper introduces a new product called the cartesian composition and discusses how various properties of the product automaton depend on the corresponding properties of the factors. A main result is that any finite connected automaton has a unique representation as a cartesian composition of prime automata.     

An improved algorithm for determinization of weighted and fuzzy automata

For a given weighted finite automaton over a strong bimonoid we construct its reduced Nerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics. We show that the reduced Nerode automaton is even smaller than the Nerode automaton, which was previously used in determinization related to this semantics. We determine necessary and sufficient conditions under which the reduced Nerode automaton is finite and provide an efficient algorithm which computes the reduced Nerode automaton whenever it is finite. In determinization of weighted finite automata over semirings and fuzzy finite automata over lattice-ordered monoids this algorithm gives smaller crisp-deterministic automata than any other known determinization algorithm.     

赋权型自动机的不同模型研究

自动机理论是理论计算机科学的基础理论之一,在很多领域自动机有着广泛的应用,有穷状态自动机是正则语言的识别机器,通常分为确定型与非确定型两种模型,其识别语言的能力是等价的。赋权自动机是另一类重要的自动机模型,自动机的每条转移规则和状态可以赋以某一代数结构上的某一数值,从而可以计算输入字符串的权值。任何有穷状态自动机都可以视为一特殊赋权自动机,因此赋权自动机功能更强大,应用更为广泛。     

Constructing finite automata with invertibility by transformation method

Ra,Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields.In a previous paper,the authors generalized Ra,Rb transformations to deal with nonlinear memory finite automata,and gave sufficient conditions for weak inverse and for weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automata satisfying one of these sufficient conditions were also given.This paper extends the concepts,methods and results to general finite automata,in which states consist of finite input history,finite output history and finite “inner state“ history.