@inproceedings{9cadf3aab8b34eabadfbee03e3733252,
title = "Negation-limited formulas",
abstract = "We give an efficient structural decomposition theorem for formulas that depends on their negation complexity and demonstrate its power with the following applications: We prove that every formula that contains t negation gates can be shrunk using a random restriction to a formula of size O(t) with the shrinkage exponent of monotone formulas. As a result, the shrinkage exponent of formulas that contain a constant number of negation gates is equal to the shrinkage exponent of monotone formulas. We give an efficient transformation of formulas with t negation gates to circuits with log t negation gates. This transformation provides a generic way to cast results for negation-limited circuits to the setting of negation-limited formulas. For example, using a result of Rossman ([33]), we obtain an average-case lower bound for formulas of polynomial-size on n variables with n1/2-∈ negations. In addition, we prove a lower bound on the number of negations required to compute one-way permutations by polynomial-size formulas.",
keywords = "De Morgan formulas, Negation complexity, Shrinkage",
author = "Siyao Guo and Ilan Komargodski",
note = "Publisher Copyright: {\textcopyright} Siyao Guo and Ilan Komargodski.; 18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015 ; Conference date: 24-08-2015 Through 26-08-2015",
year = "2015",
month = aug,
day = "1",
doi = "10.4230/LIPIcs.APPROX-RANDOM.2015.850",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "850--866",
editor = "Naveen Garg and Klaus Jansen and Anup Rao and Rolim, \{Jose D. P.\}",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015",
address = "ألمانيا",
}