关于非线性有限自动机的弱可逆性

ON WEAK INVERTIBILITY OF NONLINEAR FINITE AUTOMATA

根据ＲａＲｂ变换所得方程是否有解或至多一解可判定有限自动机Ｍ是否为弱逆或弱可逆．本文证明这些充分条件与某类映射为满射或单射是等价的，从而减少了判定所需的工作量．本文还讨论了它们同时也是判定Ｍ为弱逆或弱可逆的必要条件的情形．

For a nonlinear finite automaton, according to the solution number for equations of its RaRb transformations, there exist two sufficient criteria about its weak invertibility and weak inverse. In this paper,both sufficient criteria are studied further. It is proved that they are equivalent to the injection or surjection of some maps. Sufficient and necessary conditions about weak invertibility or weak inverse for a kind of nonlinear finite automaton are given.