Algorithmic number theory
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Inductive Inference of Recursive Functions: Complexity Bounds
Baltic Computer Science, Selected Papers
The Mathematics of Coding Theory
The Mathematics of Coding Theory
Polynomial time quantum computation with advice
Information Processing Letters
Hierarchies of memory limited computations
FOCS '65 Proceedings of the 6th Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1965)
Amount of nonconstructivity in deterministic finite automata
Theoretical Computer Science
Finite state transducers with intuition
UC'10 Proceedings of the 9th international conference on Unconventional computation
On the amount of nonconstructivity in learning recursive functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
On the amount of nonconstructivity in learning formal languages from positive data
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P.Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L. E. J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was "nonconstructive arguments have no value for mathematics". However, P. Erdös got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. R.Freivalds [7] showed that nonconstructive methods in coding theory are related to the notion of Kolmogorov complexity. We study the problem of the quantitative characterization of the amount of nonconstructiveness in nonconstructive arguments. We limit ourselves to computation by deterministic finite automata. The notion of nonconstructive computation by finite automata is introduced. Upper and lower bounds of nonconstructivity are proved.