Showing papers by "Juris Hartmanis published in 1975"
TL;DR: It is shown that translation into optimal Goedel numberings can be computationally arbitrarily complex, thus indicating that from a computer science point of view, optimal Goeden numberings have undesirable properties.
Abstract: In this paper we consider classes of Goedel numberings, viewed as simple models for programming languages, into which all other Goedel numberings can be translated by computationally simple mappings. Several such classes of Goedel numberings are defined and their properties are investigated. For example, one such class studied is the class of Goedel numberings into which all other Goedel numberings can be translated by finite automata mappings. We also compare these classes of Goedel numberings to the class of optimal Goedel numberings and show that translation into optimal Goedel numberings can be computationally arbitrarily complex, thus indicating that from a computer science point of view, optimal Goedel numberings have undesirable properties.
23 citations
13 Oct 1975
TL;DR: It is shown that the tape bounded complexity classes of languages over single letter alphabets are closed under complementation and that every infinite sla language recognizable on less than log n tape has infinitely many different regular subsets.
Abstract: In this note we show that the tape bounded complexity classes of languages over single letter alphabets are closed under complementation. We then use this result to show that there exists an infinite hierarchy of tape bounded complexity classes of sla languages between log n and log log n tape bounds. We also show that every infinite sla language recognizable on less than log n tape has infinitely many different regular subsets, and, therefore, 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.
8 citations