Algorithmic number theory
Complexity of Probabilistic Versus Deterministic Automata
Baltic Computer Science, Selected Papers
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
Amount of Nonconstructivity in Finite Automata
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Hierarchies of memory limited computations
FOCS '65 Proceedings of the 6th Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1965)
Non-constructive methods for finite probabilistic automata
DLT'07 Proceedings of the 11th international conference on Developments in language theory
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
Frequency prediction of functions
MEMICS'11 Proceedings of the 7th international conference on Mathematical and Engineering Methods in Computer Science
Hartmanis-Stearns conjecture on real time and transcendence
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
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
Multiple usage of random bits in finite automata
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
| Hi-index | 5.23 |
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. Erdos 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. The author (Freivalds, 2008) [10] 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.