Abstract
The relation between reversals and alternation is studied in two simple models of computation: the 2-counter machine with a one-way input tape whose counters make only one reversal (1-reversal 2CM) and the one-way pushdown automaton whose pushdown store makes only one reversal (1-reversal PDA). The following is shown: (a) alternating 1-reversal 2CM’s accept all recursively enumerable languages; (b) alternating 1-reversal PDA’s accept exactly the languages accepted by exponential time-bounded deterministic TM’s. The first improves on the known result that alternating 1-reversal 4CM’s accept all recursively enumerable languages. The second improves an earlier result that alternating PDA’s with no restrictions on reversals accept exactly the exponential-time languages.
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