## Journal of the Franklin Institute, Volume 339Pergamon Press, 2002 Vols. 1-69 include more or less complete patent reports of the U. S. Patent Office for years 1825-1859. cf. Index to v. 1-120 of the Journal, p. [415] |

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**semigroup**, which implies that every finite semiautomaton can be simulated by a**semigroup**machine [ 21 ] . 4.1 . Fault - tolerant group machines The next - state function of a group machine G is given by 86 ( 91 , 92 ) = 91 ° 92 , where ...Page 407

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**semigroup**machines : Definition . A redundant implementation for a**semigroup**machine ( S , ) is a**semigroup**machine ( H , ◇ ) that concurrently simulates S in the following sense : there exist a one - to - one mapping : S ' → S ...Page 413

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**semigroup**T of T is isomorphic to S / ~ for a congruence relation ~ on**semigroup**S ( the**semigroup**of machine S ) . In other words , there exists a homomorphism л : ST such that Т = л ( S ) . Proof . From Eq . ( 8 ) , we see that T is ...### Contents

Contents | 1 |

Vol 339 No 2 MARCH 2002 | 129 |

PERGAMON ISSN 00160032 | 248 |

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2002 The Franklin adaptive algorithm analysis angiogenesis applied approach Benjamin Franklin Medal Chebyshev Chebyshev polynomials chirp closed-loop computation consider constraints corresponding coset defined denote detection domain dynamic systems Elsevier Science Ltd encoding energy equation estimation example fault fault-tolerant feedback finite flywheel Franklin Institute Franklin Institute 339 Franklin Institute www.elsevier.com/locate/jfranklin frequency response frequency response functions gain given group machine homomorphism IEEE IEEE Trans implementation input k₁ mapping Mathematics matrix method NARMAX model noise nomograph nonlinear systems observer obtained optimal control optimal control problem output packet paleomagnetic paper parameters performance Petri net phase error PID controller polynomials proposed Published by Elsevier quadratic redundant residual ScienceDirect Section selectivity semiautomata semigroup shown in Fig signal processing simulation solution solve SPRO stability T₁ TDTL Theorem trajectories transfer function transform transitional filter University v₁ variables vector Widrow zero