Abstract: | Set logic algebra (SLA) is a special case of multiple-valued logic algebra. As an ultra higher-valued logic system, a set-valued logic (SVL) system offers a potential and an essential solution to the interconnection problems that occur in highly parallel VLSI systems. The fundamental concept inherent to a SVL system is multiplex computing or logic values multiplexing: which means the simultaneous transmission of logic values. This basic concept enables the realization of superchips free from interconnection problems. Parallel processing with multiplexable information carriers makes possible to construct large-scale highly parallel system with reduced interconnections. Since the multiplexing of logic values increases the information density, several binary functions can be executed in parallel in a single module. Therefore a great reduction of interconnections can be achieved using optimal multiplexing scheme. Possible approaches to the implementation of the SVL system are based on frequencies multiplexing, waves multiplexing and molecules multiplexing, and are called carrier computing systems. Our research focuses on the study of completeness properties in SLA under compositions with union ($\bigcup$), intersection ($\bigcap$) and complement ($\sp-$) functions. More precisely, the question is what kind of set logic functions can be constructed from given set of functions which includes $\bigcup,$ $\bigcap,$ and $\sp-,$ i.e. whether any set logic function can be constructed from such set. We classify the set logic functions according to their ability to participate in a base (complete irredundant sets of functions) and describe all bases once the classification is done. We develop also some algorithms (programs) for classification and enumeration of functions and bases, which are very useful for a general completeness analysis. |