A Note on Cooperating Systems of One-Way Alternating Finite Automata with Only Universal States

A cooperating system of finite automata (CS-FA) has more than one finite automata (FA's) and an input tape. These FA's operate independently on the input tape and can communicate with each other on the same cell of the input tape. For each k greater than or equal to 1, let L[CS-1DFA(k)] (L[CS-1UFA(k)]) be the class of sets accepted by CS-FA's with k one-way deterministic finite automata (alternating finite automata with only universal states). We show that L[CS-1DFA(k+1)] - L[CS-1UFA(k)] [ne] [empty_set] and L[CS-1UFA(2)] - [cup] sub(1 less than or equal to )k< infinity [CS-1DFA(k)] [ne] [empty_set].