On Reversal Bounded Alternating Turing Machines

Abstract It is known that, for one-tape nondeterministic Turing machines, S ( n )-space and S ( n )-reversal bounded machines ( S ( n ) ⩾ n ) recognize the same class of languages. We present a simulation of S ( n )-space bounded alternating Turing machines (ATM) by one-tape lg ∗ S ( n )-reversal bounded ATMs. We also show that ATMs making a constant number of reversals recognize only regular languages. This shows that there is a striking difference in computational power between machines making a constant number of reversals and those making an ‘almost’ constant (i.e., lg ∗ n ) number of reversals.

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