The Problem Of Freedom On Submonoid Of Strong Left Singular Language And Preserving Homomorphism

This thesis contains two main research contents. One is the problem of freedom on certain subsemigroups of the submonoid of strong left singular language. The other is homomorphism which preserve certain families of languages and some codes. In2004, Chunhua Cao showed that certain subsemigroups of the submonoid of left singular language is unfree. In this thesis, we prove three main conclusion. The first one is that certain subsemigroups of the submonoid of strong left singular language is unfree. The second one is a family of languages which are not only a strong left singular language but also a right cancellative language is free. The last one is that for any finite language we can find a word to makes product is a strong left singular language. For homomorphism which preserve certain families of languages, H.J. Shyr and Z.Z. Li prouved the homomorphism which preserve the primitive pritimitive word, pure code, comma-free code, infix code, noncounting language, power-separating language. In2002Japanese scholar T. Moriya proposed the notion of w-infix code, s-infix code, h-infix code and in2010Taiwan scholars H.J. Shyr, Chen-Ming Fan, C.C. Huang given anti-automatic dense language. We get the homomorphism which preserves w-infix code, s-infix code, h-infix code and anti-automatic dense language. In addition, we obtain a necessary and sufficient condition for homomorphism preserving2-code.