Two methods of augmenting the structure of a sequential machine so that it is diagnosable are presented. The checkable (checking sequences) and repeated symbol distinguishing sequences (RDS) are discussed. It was found that as few as twice the number of outputs of the given machine is sufficient for constructing a state-output augmentation with RDS. Techniques for minimizing the number of states in resolving convergences and in resolving equivalent and nonreduced cycles are developed.

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Algebraic Structure Theory of Sequential Machines

Augmentation of machine structure to improve its diagnosability

Homomorphic simplification is one way of defining valid simplication of deterministic models. To allow the use of similar techniques for probabilistic systems, we introduce the concept of an ergodic machine. An ergodic machine is a specification for a deterministic system and it represents and associated probabilistic system when viewed properly. The probabilistic features arise by using an ergodic transformation on a “hidden” partial state space. An ergodic transformation can be thought of as an ideal random number generator. In this paper, we develop the concepts of ergodic machines necessary for faithfully representing probabilistic systems and make connections to markov chains and pseudo random number generators.

Algebraic Structure Theory of Sequential Machines

Citations

Augmentation of machine structure to improve its diagnosability

Deterministic representation of probabilistic systems by ergodic machines

TH ` ESE DE DOCTORAT DOMAINE : STIC Sp´´ : Informatique

Formalizing the design-trajectory of sequential machines

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