Abstract
Prenex formulas of RPC are examined; all formulas obtained one from the other by renamings of objective and predicate variables and by deletion of fictitious quantifiers are reckoned to be alike. The number of occurrences of atomic formulas is called the length of a formula;
denotes the number of formulas in a set
, having length n.
is said to be approximatable by deducibility if an algorithmexists which for each positive ɛ yields a solvable set N of formulas and a number
such that
for all
. The number
is called the deducibility number of the class A of formulas if the sequence
where à is the set of deducible formulas from A, effectively converges to α. The deducibility number is found, or, at least, approximatability is proved, for a number of known reduction classes in RPC. Two items of literature are cited.
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Literature cited
Ya. M. Barzdin', “On the frequency solution of algorithmically unsolvable mass problems,” Dokl. Akad. Nauk SSSR,191, No. 5, 967–970 (1970).
Yu. Sh. Gurevich, “On effective recognition of the realizability of formulas of RPC,” Algebra Logika,5, No. 2, 25–55 (1966).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 60, pp. 103–108, 1976. Results announced November 13, 1975.
In conclusion, I am deeply grateful to S. Yu. Maslov for attention to the work and for valuable advice.
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Norgela, S.A. On the approximation of reduction classes of RPC by decidable classes. J Math Sci 14, 1493–1496 (1980). https://doi.org/10.1007/BF01693982
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DOI: https://doi.org/10.1007/BF01693982