Universal Boolean Systems

Abstract

Boolean interaction systems and hard interaction systems define nets of interacting cells. They are based on the same local interaction principle between two cells as interaction nets but do not allow that the structure of nets may evolve. With boolean nets, it is not possible to create or destroy cells or links between existing cells. They are very similar to hardware circuits but based on an implicit rendez-vous information exchange mechanism.If we want to implement such systems using hardware circuits, it is important to define a set of universal combinators that reduces this task to the implementation of a fixed number of known agents. Here, we show how we can simulate every hard interaction system by a universal boolean interaction system composed of three combinators: a duplicator, a NAND gate and a three-state input/output channel.