Abstract
This expository paper describes some of the results of two recent research papers [GOP+05, GPSZ05]. The first of these papers proves that every NP-complete set is many-one autoreducible. The second paper proves that every many-one autoreducible set is many-one mitotic. It follows immediately that every NP-complete set is many-one mitotic. Hence, we have the compelling result that every NP-complete set A splits into two NP-complete sets A 1 and A 2.
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
Ambos-Spies, K.: P-mitotic sets. In: Börger, E., Hasenjäger, G., Roding, D. (eds.) Logic and Machines. LNCS, vol. 177, pp. 1–23. Springer, Heidelberg (1984)
Beigel, R., Feigenbaum, J.: On being incoherent without being very hard. Computational Complexity 2, 1–17 (1992)
Buhrman, H., Fortnow, L., van Melkebeek, D., Torenvliet, L.: Using autoreducibility to separate complexity classes. SIAM Journal on Computing 29(5), 1497–1520 (2000)
Buhrman, H., Hoene, A., Torenvliet, L.: Splittings, robustness, and structure of complete sets. SIAM Journal on Computing 27, 637–653 (1998)
Buhrman, H., Torenvliet, L.: On the structure of complete sets. In: Proceedings 9th Structure in Complexity Theory, pp. 118–133 (1994)
Glasser, C., Ogihara, M., Pavan, A., Selman, A., Zhang, L.: Autoreducibility, mitoticity, and immunity. In: Proceedings of the 30th International Symposium onMathematical Foundations of Computer Science. LNCS, vol. 3618, Springer, Heidelberg (2005)
Glasser, C., Pavan, A., Selman, A., Zhang, L.: Redundancy in complete sets. Technical Report 05-068, Electronic Colloquium on Computational Complexity (2005)
Ladner, R.: Mitotic recursively enumerable sets. Journal of Symbolic Logic 38(2), 199–211 (1973)
Ogiwara, M., Watanabe, O.: On polynomial-time bounded truth-table reducibility of NP sets to sparse sets. SIAM Journal of Computing 20(3), 471–483 (1991)
Trakhtenbrot, B.: On autoreducibility. Dokl. Akad. Nauk SSSR 192, (1970); Translation in Soviet Math. Dokl. 11, 814– 817 (1970)
Yao, A.: Coherent functions and program checkers. In: Proceedings of the 22nd Annual Symposium on Theory of Computing, pp. 89–94 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Glaßer, C., Pavan, A., Selman, A.L., Zhang, L. (2006). Mitosis in Computational Complexity. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_4
Download citation
DOI: https://doi.org/10.1007/11750321_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
eBook Packages: Computer ScienceComputer Science (R0)