On Tape Bounds for Single Letter Alphabet Language Processing

Abstract In this paper we show that the tape bounded complexity classes of languages over single letter alphabets (sla) are closed under complementation. We then use this results to show by means of diagonalization that there exists an infinite hierarchy of tape bounded complexity classes of sla languages between log log n and log n tape bounds. On the other hand, we show that the power of diagonalization over sla inputs with less than log n tape is very limited by proving that every infinite sla language accepted using less than log n tape contains infinite regular subsets. From this result it immediately follows that the set of primes in unary notation, P, requires exactly log n tape for its recognition and every infinite subset of P requires at least log n tape.