## Algebraic structure theory of sequential machines |

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### Contents

LOOPFREE STRUCTURE | 97 |

STATE SPLITTING 11 9 | 119 |

FEEDBACK AND ERRORS 1 48 | 148 |

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### Common terms and phrases

applied assigned according behavior realization blocks of f chapter choose clock closed sets component machines concept congruence relation consider machine construction contains Corollary corresponding cosets d.c. conditions define Definition 3.4 distributive lattice element equations equivalence relation equivalent example EXERCISE exists feedback finite flow table front machine group accumulator homomorphic image identity map implies input sequence isomorphic Lemma loop-free machine F machine Mx Mealy machine Moore machine n-state machine nonredundant normal subgroup notation obtain one-to-one operator output consistent S.P. P-R machine pair algebra parallel decomposition partially ordered set partition pair realization of machine reduced machine reduced realization result right cosets S.P. lattice satisfy schematic semigroup sequential machine serial connection serial decomposition set of partitions shown in Fig simple group strongly connected sublattice subset system pair tail machine temporary errors Theorem Theorem 7.6 transitions variables