# 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))*, *SUTM(S(n))*, *1SATM(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 \(\mathcal{L}(1DSA(n)FA) \subset \mathcal{L}(1DSA(n + 1)FA)\) for all *n*>0, and show that \(\mathcal{L}(1DFA(2)) - \cup _{k = 1}^\infty \mathcal{L}(DSA(k)FA) \ne \not 0\), where *DFA(k)* denotes deterministic *k*-head finite automata. Finally we investigate closure properties under Boolean operations for some of these classes of languages.

## Keywords

Turing Machine Binary String Computation Tree Finite Automaton Kolmogorov Complexity## Preview

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