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Linear SpeedUp, Information Vicinity, and FiniteState Machines
 In IFIP proceedings. NorthHolland
, 1994
"... Connections are shown between two properties of a machine model: linear speedup and polynomial vicinity . In the context of the author's Block Move (BM) model, these relate to: "How long does it take to simulate a finite transducer S on a given input z?" This question is related to t ..."
Abstract

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Connections are shown between two properties of a machine model: linear speedup and polynomial vicinity . In the context of the author's Block Move (BM) model, these relate to: "How long does it take to simulate a finite transducer S on a given input z?" This question is related to the centuryold problem of finding economical representations for finite groups. Under some cost measures for computing S(z), the BM enjoys the linear speedup property, but under morerealistic measures, and subject to a reasonable but unproved hypothesis, it has the antithetical property of a constantfactor time hierarchy . 1 SpeedUp and Vicinity Hartmanis and Stearns [HS65] proved that the standard multitape Turing machine (TM) model enjoys the following property, for which we give a general statement: Definition 1.1. A machine model M has the linear speedup property if there exists k 0 ? 0 such that for every ffl ? 0 and t(n) timebounded Mmachine M , there exists a Mmachine M 0 that computes...
1. SpeedUp and Vicinity
"... Connections are shown between two properties of a machine model: linear speedup and polynomial vicinity. In the context of the author’s Block Move (BM) model, these relate to: “How long does it take to simulate a finite transducer S on a given input z? ” This question is related to the centuryold ..."
Abstract
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Connections are shown between two properties of a machine model: linear speedup and polynomial vicinity. In the context of the author’s Block Move (BM) model, these relate to: “How long does it take to simulate a finite transducer S on a given input z? ” This question is related to the centuryold problem of finding economical representations for finite groups. Under some cost measures for computing S(z), the BM enjoys the linear speedup property, but under morerealistic measures, and subject to a reasonable but unproved hypothesis, it has the antithetical property of a constantfactor time hierarchy.