${\text{ASPACE}}(o(\log \log n))$ is Regular

Abstract

One of the common results of resource bounded Turing machines is the $\log \log n$ lower bound for the space usage of deterministic and nondeterministic Turing machines that accept nonregular languages. In this paper this result is extended to alternating Turing machines: It is proved that if $f(n) = o(\log \log n)$, then $f(n)$-space-bounded (off-line) alternating Turing machines can accept only regular sets. The problem has been open for a decade.