Geodesic
Boolean reducibility
Diskretnaya Matematika, Tome 15 (2003) no. 3, pp. 40-53

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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 $\mathcal L_Q$ of all $Q$-degrees, namely, the existence of maximal, minimal and the greatest elements, infinite chains and antichains, and upper bounds. The research was supported by the Russian Foundation for Basic Research, grant 03–01–00783. 
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     author = {S. S. Marchenkov},
     title = {Boolean reducibility},
     journal = {Diskretnaya Matematika},
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     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2003_15_3_a1/}
}
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S. S. Marchenkov. Boolean reducibility. Diskretnaya Matematika, Tome 15 (2003) no. 3, pp. 40-53. http://geodesic.mathdoc.fr/item/DM_2003_15_3_a1/