NDLI: On feasible numbers (Preliminary Version)

Content Provider	ACM Digital Library
Author	Simon, Janos
Abstract	We study complexity problems associated with generation and manipulation of integers. We show that many such questions may be formulated as problems about random access machines (RAMs), and recent results about RAMs with special instructions sets can be used to give estimates about the complexity of the manipulations. Finally we settle an open problem about RAMs (which becomes more interesting in this setting), namely the power of unrestricted vector machines, studied in [5] [6] [2]. We prove that allowing arbitrary shifts (instead of bounded shifts) gives at most a polynomial reduction in the time necessary to recognize languages by vector machines, thus solving the main problem left unanswered by the papers of Pratt and Stockmeyer [5], [6] and Hartmanis and Simon [2], [3]. Equivalently, it is possible to compare two integers, each obtained by a sequence of at most n operations of shift, sum, and boolean vector operations, within tape polynomial in n.
Starting Page	195
Ending Page	207
Page Count	13
File Format	PDF
DOI	10.1145/800105.803409
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1977-05-04
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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On feasible numbers (Preliminary Version)