Abstract
We study the power of reversal-bounded ATMs (alternating Turing machines). The results obtained are as follows: (1) Every recursively enumerable set can be accepted by a 1-tape-1-counter ATM which runs in constant reversals (which are the number of times a head changes direction) but not by any 1-tape-1-counter NTM (nondeterministic TM) which runs in constant reversals, where a 1-tape-1-counter ATM (NTM, respectively) is a 1-tape ATM (NTM, respectively) with one counter tape. (2) For functions B ( n ) and R ( n ) satisfying B ( n ) ≦ 2 O ( R ( n )) and B(n) R(n) ≧ n , a class of languages accepted by 1-tape ATMs which run in O ( R ( n )) reversal and O ( B ( n )) leaf simultaneously is equivalent to a class of languages accepted by NTMs which run in O ( B ( n ) R ( n )) space.
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