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Journal of Computer Science and Technology

, Volume 4, Issue 2, pp 163–171 | Cite as

On the structure of binary feedforward inverses with delay 2

  • Zhu Xinjie 
Regular Papers

Abstract

LetM′ = C(M α, ƒ) be a semi-input-memory finite automaton with input alphabetY and output alpha-betX. IfX=Y={0, 1}, thenM′ is a feedforward inverse with delay 2 if and only if there exists a cycleC of state diagram ofM α such that ƒ(y o , ...,y c , λα (t)) can be expressed in the form of ƒ(1) (y 0, ...,y c − 1,y α (t)) ⊕y c for any statet inC andy o, yl, ... yc inY; or of ƒ(2) (y 0, ...,y c − 2,y α (t)) ⊕y c − 1 for any statet inC andy o, yl, ..., yc inY; or for any statet inC andy o, yl, ..., yc, inY, y o yl ... yc satisfies the D [t] condition. The socalledy o yl ... yc satisfying the D [t] condition is that: for somei, j, (i, j)∈{(1,2), (1, 3), (2,1), (2,2), (3,1), (3,2)}, there exists a (c+2−k)—ary functionf (k), k=1, 2, 3, such that the Equation (1) and Equation (2) hold simultaneously for ally c −2/′ , ...,y c +1/′ Y.
where\(\hat t = \delta _\alpha \left( t \right)\); and if (i, j)=(1,2), then one and only one of the following conditions C1 and C2 holds for ally c −1/′ ,y c ,y c +1/′ Y.
Condition C1: there exists ac-ary functiong (1), such that
Condition C2: there exists a (c−1)-ary functiong (2), such that
, where\(\hat t = \delta _\alpha \left( t \right)\).

Keywords

State Diagram Finite Automaton Closure Property Channel Error Input Alphabet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Tao Renji, Relationship between bounded error propagation and feedforward invertibility.Kexue Tongbao,27: 6 (1982), 680–682.MATHMathSciNetGoogle Scholar
  2. [2]
    Tao Renji, Some results on the structure of feedforward inverses,Sientia Sinica (Series A),27: 2 (1984), 157–162.MATHGoogle Scholar
  3. [3]
    Tao Renji, Invertibility of Finite Automata, Science Press, Beijing, 1979 (in Chinese).MATHGoogle Scholar
  4. [4]
    Tao Renji and Chen Shihua, Some properties on the structure of invertible and inverse finite automata with delay τ,Chinese Journal of Computers,3: 4 (1980), 289–297.Google Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 1989

Authors and Affiliations

  • Zhu Xinjie 
    • 1
  1. 1.Institute of SoftwareAcademia SinicaBeijingChina

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