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


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\(\hat t = \delta _\alpha \left( t \right)\).


State Diagram Finite Automaton Closure Property Channel Error Input Alphabet 
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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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