Abstract
We deal with frequency computations in polynomial time, or more generally with resource bounded frequency computations. We investigate the first non-trivial case of the Hinrichs-Wechsung conjecture, which states that as soon as we have at least 2d + d inputs to be queried, it does not become harder to get an answer with at most d errors, if we increase the number of inputs to be queried. This conjecture can easily be seen to hold for cases d < 3, and it seems very hard to prove in general. We solve the problem affirmatively in the case d = 3 by a combination of theoretical reasoning with a highly optimized computer search.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Austinat, H., Diekert, V., Hertrampf, U.: A Structural Property of Regular Frequency Computations. Theor. Comp. Sc. 292(1), 33–43 (2003)
Austinat, H., Diekert, V., Hertrampf, U., Petersen, H.: Regular Frequency Computations. In: RIMS Symposium on Algebraic Systems, Formal Languages and Computation, Kyoto, Japan, pp. 35–42 (2000)
Beigel, R., Gasarch, W.I., Kinber, E.B.: Frequency Computation and Bounded Queries. Theor. Comp. Sc. 163(1–2), 177–192 (1996)
Degtev, A.N.: On (m,n)-Computable Sets. Algebraic Systems, 88–99 (1981) (in Russian)
Hinrichs, M., Wechsung, G.: Time Bounded Frequency Computations. Information and Computation 139(2), 234–257 (1997)
Kinber, E.B.: Frequency Calculations of General Recursive Predicates and Frequency Enumeration of Sets. Soviet Mathematics Doklady 13, 873–876 (1972)
Kinber, E.B.: On Frequency-Enumerable Sets. Algebra i Logika 13, 398–419 (1974) (in Russian); English translation in Algebra and Logic 13, 226–237 (1974)
Kinber, E.B.: Frequency Computations in Finite Automata. Kibernetika 2, 7–15 (1976) (in Russian); English translation in Cybernetics 12, 179–187 (1976)
Kummer, M., Stephan, F.: The Power of Frequency Computation. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 969, pp. 323–332. Springer, Heidelberg (1995)
Kummer, M., Stephan, F.: Recursion Theoretic Properties of Frequency Computation and Bounded Queries. Information and Computation 120, 59–77 (1995)
Kummer, M.: A Proof of Beigel’s Cardinality Conjecture. J. of Symbolic Logic 57(2), 677–681 (1992)
McNaughton, R.: The Theory of Automata, a Survey. Advances in Computers 2, 379–421 (1961)
McNicholl, T.: The Inclusion Problem for Generalized Frequency Classes. PhD thesis, George Washington University, Washington (1995)
Rose, G.F.: An Extended Notion of Computability, Abstracts Int. Congress for Logic, Methodology, and Philosophy of Science. Stanford, California, p. 14 (1960)
Tantau, T.: Towards a Cardinality Theorem for Finite Automata. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 625–636. Springer, Heidelberg (2002)
Trakhtenbrot, B.A.: On the Frequency Computation of Functions. Algebra i Logika 2, 25–32 (1963) (in Russian)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hertrampf, U., Minnameier, C. (2008). Resource Bounded Frequency Computations with Three Errors. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-69733-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69732-9
Online ISBN: 978-3-540-69733-6
eBook Packages: Computer ScienceComputer Science (R0)