On multiple-valued logical functions realized by asynchronous sequential circuits

This paper concerns multiple-valued logical function realized by asynchronous circuit that may have ''feedback loops'' and its completeness problems. The first aim is to give mathematical definition of an asynchronous circuit over multiple-valued logical funcitons and of the realization of multiple-valued logical function by means of an asynchronous circuit. For asynchronous element, the definition of circuit construction and initialization are very sensitive. A slight modification may have a considerable influence on the completeness. We consider three types of completeness (LF-, GS-: NS-completeness) for a set of multiple-valued logical functions. The LF-completeness means completenss of logical functions realized ''loop-free'' cirucit. The GS-completeness means completeness under general initialization assumption. The NS-completeness measn completeness under initialization by input assumption. The second aim is to give a completeness criterion for each type of completeness. This aim is realized for LF-completeness in general case and GS-completeness in ternary case. A completenss criteria for GS-completenss and NS-completeness are given under strong conditions.