The intersection and the union of the asynchronous systems

The asynchronous systems f are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input u : R → {0, 1} a set of states x ∈ f(u), where x : R → {0, 1}. The intersection of the systems allows adding supplementary conditions in modeling and the union of the systems allows considering the validity of one of two systems in modeling, for example when testing the asynchronous circuits and the circuit is supposed to be ’good’ or ’bad’. The purpose of the paper is that of analyzing the intersection and the union against the initial/final states, initial/final time, initial/final state functions, subsystems, dual systems, inverse systems, Cartesian product of systems, parallel connection and serial connection of systems. Rezumat Sistemele asincrone f sunt modelele circuitelor asincrone din electronica digitala. Ele sunt functii multivoce care asociaza fiecarei intrari u : R → {0, 1} o multime de stari x ∈ f(u), unde x : R → {0, 1}. Intersectia sistemelor permite adaugarea de conditii suplimentare in modelare si reuniunea sistemelor permite considerarea validitatii unui sistem din doua in modelare, de exemplu cand se testeaza circuitele asincrone si circuitul se presupune a fi ’bun’ sau ’rau’. Scopul lucrarii e acela de a analiza intersectia si reuniunea raportate la starile initiale/finale, timpul initial/final, functiile stare initiala/finala, subsisteme, sisteme duale, sisteme inverse, produs cartezian al sistemelor, legare in paralel si legare in serie a sistemelor. MSC2000: 93C62, 94C10