Resource Bounded Frequency Computations with Three Errors
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 2 d + 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.
KeywordsFrequency Computation Finite Automaton Full Paper Partial Matrice Partial Matrix
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- 2.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)Google Scholar
- 4.Degtev, A.N.: On (m,n)-Computable Sets. Algebraic Systems, 88–99 (1981) (in Russian) Google Scholar
- 9.Kummer, M., Stephan, F.: The Power of Frequency Computation. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 969, pp. 323–332. Springer, Heidelberg (1995)Google Scholar
- 13.McNicholl, T.: The Inclusion Problem for Generalized Frequency Classes. PhD thesis, George Washington University, Washington (1995)Google Scholar
- 14.Rose, G.F.: An Extended Notion of Computability, Abstracts Int. Congress for Logic, Methodology, and Philosophy of Science. Stanford, California, p. 14 (1960)Google Scholar