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Showing papers by "Juris Hartmanis published in 1974"


Proceedings ArticleDOI
01 Apr 1974
TL;DR: It is proved that, counting one operation as a unit of time and considering the machines as acceptors, deterministic and nondeterministic polynomial time acceptable languages are the same, and are exactly the languages recognizable in polynomially tape by Turing machines.
Abstract: We consider random access machines with a multiplication operation, having the added capability of computing logical operations on register are considered both as an integer and as a vector of bits and both arithmetic and boolean operations may be used on the same register. We prove that, counting one operation as a unit of time and considering the machines as acceptors, deterministic and nondeterministic polynomial time acceptable languages are the same, and are exactly the languages recognizable in polynomial tape by Turing machines. We observe that the same measure on machines without multiplication is polynomially related to Turing machine time-thus the added computational power due to multiplication in random access machines is equivalent to the computational power which polynomially tape-bounded Turing machine computations have over polynomially time-bounded computations. Therefore, in this formulation, it is not harder to multiply than to add if and only if PTAPE = PTIME for Turing machines. We also discuss other instruction sets for random access machines and their computational power.

101 citations


Book ChapterDOI
TL;DR: The purpose of this paper is to give the reader an overview of these developments, an insight into some of these results and applications, as well as an appreciation of the unity and structure which has emerged in this area of research.
Abstract: During the last four years research on the lower level computational complexity has yielded a rich set of interesting results which have revealed deep and unexpected connections between various problems and thus brought new unity to this area of computer science. This work has also yielded new techniques and insights which are likely to have further applications, and it has identified some very central problems in the quantitative theory of computing. The purpose of this paper is to give the reader an overview of these developments, an insight into some of these results and applications, as well as an appreciation of the unity and structure which has emerged in this area of research.

22 citations


Book ChapterDOI
29 Jul 1974
TL;DR: It is shown that translation into optimal Goedel numberings can be computationally arbitrarily complex, 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 automatic 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

18 citations


Journal ArticleDOI
TL;DR: A mathematical model is defined for the study of quantitative problems about translations between universal languages and the efficiency of the translated algorithms, the optimality of translations and the complexity of the translation process between different languages.
Abstract: The purpose of this paper is to define a mathematical model for the study of quantitative problems about translations between universal languages and to investigate such problems. The results derived in this paper deal with the efficiency of the translated algorithms, the optimality of translations and the complexity of the translation process between different languages.

5 citations