EQUIVALENCES BETWEEN PROBABILISTIC SEQUENTIAL MACHINES.
MICHIGAN UNIV ANN ARBOR COLL OF LITERATURE SCIENCE AND THE ARTS
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New definitions are introduced of behavioral equivalences, and relationships are shown among the various notions of behavioral equivalence between probabilistic machines. Four basic problems are discussed for several different behavioral equivalences between machines. In what follows the symbol is a variable denoting one of the several behavioral equivelances considered. Given an arbitrary probabilistic sequential machine A 1 Is there an input-state calculable machine A a machine with deterministic switching and random outputs such that A A. 2 What are the machines A with minimal number of states such that A A. 3 How does one obtain all stable modifications of A, i.e., all machines A such that the switching probabilities of A and A differ but A A. 4 Is there a finite bound on the length of experiments required to establish whether A A holds. The four basic problems are solved completely for some equivalences between machines and are left open for other equivalences. Some applications are made to optimal control problems. Author
- Statistics and Probability
- Computer Hardware