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Boolean reducibility
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S. S. Marchenkov
Published/Copyright:
August 1, 2003
We define the operator of Boolean reducibility on the set of all infinite binary sequences. This operator is a variant of the operator of finite-automaton transformability when automata with several inputs and one state are considered. Each set Q of Boolean functions containing a selector function and closed with respect to the operation of superposition of a special form defines the Q-reducibility and Q-degrees, that is, the sets of Q-equivalent sequences. We study properties of the partially ordered set ℒQ of all Q-degrees, namely, the existence of maximal, minimal and the greatest elements, infinite chains and antichains, and upper bounds.
Published Online: 2003-08-01
Published in Print: 2003-08-01
Copyright 2003, Walter de Gruyter
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Articles in the same Issue
- Boolean reducibility
- On the complexity of testing primality by homogeneous structures
- On distinguishability of states of automata
- On glueing states of an automaton
- Almost layer-finiteness of the periodic part of groups without involutions
- The structure and methods of generation of closed classes of graphs
- On asymptotic expansions for the distributions of the number of cycles in a random permutation
