On space-bounded synchronized alternating turing machines

Abstract

We continue the study of the computational power of synchronized alternating Turing machines (SATM), introduced in [Hro86, Slo87, Slo88a, Slo88b] to allow communication via synchronization among processes of alternating Turing machines. We compare the classes of languages accepted by the four main classes of space-bounded synchronized alternating Turing machines obtained by adding or removing off-line capability and nondeterminism (1SUTM(S(n)), SVTM(S(n)), lSATM(S(n)), and SATM(S(n))). We show various strict inclusions, equalities, and incomparabilities between these classes and those accepted by plain and modified alternating Turing machines. For deterministic synchronized alternating finite automata with at most k processes (1DSA(k)FA and DSA(k)FA) we establish a tight hierarchy on the number of processes for the one-way case, namely L(1DSA(n)FA) ⊂ (1DSA(n+l)FA) for all n > 0, and show that L(1DFA(2)) -U∞k=1 L(DSA(k)FA) ≠ θ, where DFA(k) denotes deterministic Ar-head finite automata. Finally we investigate closure properties under Boolean operations for some of these classes of languages.