## The Combination Lock Version of a Finite State Machine |

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### Contents

Basic Notations and Definitions | 4 |

Deriving a Combination Lock Version | 8 |

Properties of the Combination Lock Version | 39 |

2 other sections not shown

### Common terms and phrases

0-successor algorithm 1C algorithm IC application of algorithm Automata automata theory block characterizing sequences checking experiments combination lock version consider Definition derived by algorithm different output sequences distinguishing sequence execution of line exists an input finite state machine Hence homomorphic image immediate predecessor immediate successor information lossless information lossy input sequence input string isomorphic jt(C Key Variables Kohavi longest possible combination lossless of order machine Mp multiple combination lock n-state machine opposite outputs ordered pair prefix proof of Theorem Q.E.D. Lemma Q.E.D. Theorem reduced form remove one combination resolving sequence S.P. partition s2 0 Figure s2 sl s3 second subscript Sequential Circuits Sequential Machines set of characterizing singly generated submachine sl s2 sl sl strongly connected substitution property successors with opposite suffix synchronizing sequence Theorem 3.3 tion transition unlocking Values of Key version of machine x-successor