Trading reversals for alternation

The relation between reversals and alternation is studied in two simple models of computation: the two-counter machine with a one-way input tape whose counters make only one reversal (1-reversal 2CM) and the one-way pushdown automation whose pushdown store makes only one reversal (1-reversal PDA). It is known that nondeterministic 1-reversal 2CMs (and, more generally, 1-reversal mCMs when there are m counters, m>0) can be simulated by a log n space-bounded nondeterministic TMs, and nondeterministic 1-reversal PDAs accept exactly the linear context-free languages. When nondeterministic is generalized to alternating, it is shown that alternating 1-reversal 2CMs accept all recursively enumerable languages and that alternating 1-reversal PDAs accept exactly the languages accepted by exponential time-bonded deterministic TMs. Since deterministic 2CMs with unrestricted counters accept all recursively enumerable languages, the first results show that reversals can be traded for alternation