Which bases admit non-trivial shrinkage of formulae?

Computational Complexity

Volumn 10, Issue 1, 2001, Pages 28-40

  Chockler, Hana ^a   Zwick, Uri ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Boolean functions; Formula complexity; Lower bounds; Random restrictions; Shrinkage exponents

Indexed keywords

EID: 0035729272     PISSN: 10163328     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001610     Document Type: Article

References (14)

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2. A. E. ANDREEV (1987). On a method for obtaining more than quadratic effective lower bounds for the complexity of π-schemes. Vestnik Moskov. Univ. Mat. 1987, 70-73 (in Russian). English translation in Moscow Univ. Math. Bull. 42, 63-66.
3. H. CHOCKLER & U. ZWICK (2001). Which formulae shrink under random restrictions? In Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms (SODA'01) (Washington, D.C.), 702-708.
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10. E. L. POST (1941). The Two-Valued Iterative Systems of Mathematical Logic. Ann. of Math. Stud. 5, Princeton Univ. Press.
11. M. M. ROKHLINA (1970). The schemes that increase reliability. Problemy Kibernetiki 23, 295-301 (in Russian).
12. B. A. SUBBOTOVSKAYA (1961). Realizations of linear functions by formulas using +, *, -. Dokl. Akad. Nauk SSSR 136, 553-555 (in Russian). English translation in Soviet Math. Dokl. 2, 110-112.
13. B. A. SUBBOTOVSKAYA (1961). Realizations of linear functions by formulas using +, *, -. Dokl. Akad. Nauk SSSR 136, 553-555 (in Russian). English translation in Soviet Math. Dokl. 2, 110-112.
14. L. G. VALIANT (1984). Short monotone formulae for the majority function. J. Algorithms 5, 363-366.