The limits of depth reduction for arithmetic formulas

DOI10.1145/2591796.2591827zbMath1315.68141OpenAlexW2002803848MaRDI QIDQ5259547

Mrinal Kumar, Shubhangi Saraf

Publication date: 26 June 2015

Published in: Proceedings of the forty-sixth annual ACM symposium on Theory of computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/2591796.2591827

zbMATH Keywords

lower boundsdepth reductionarithmetic formulashifted partial derivatives

Mathematics Subject Classification ID

Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)

Related Items

Lower Bounds for Sums of Powers of Low Degree Univariates ⋮ On the limits of depth reduction at depth 3 over small finite fields ⋮ The Shifted Partial Derivative Complexity of Elementary Symmetric Polynomials ⋮ Lower Bounds for Depth-4 Formulas Computing Iterated Matrix Multiplication ⋮ An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas ⋮ On the Power of Homogeneous Depth 4 Arithmetic Circuits ⋮ The Computational Power of Depth Five Arithmetic Circuits ⋮ Lower bounds by Birkhoff interpolation ⋮ Depth-4 lower bounds, determinantal complexity: a unified approach

Uses Software

• SuLQ

Cites Work

• Unnamed Item
• Unnamed Item
• Efficient algorithms for privately releasing marginals via convex relaxations
• The Geometry of Differential Privacy: The Small Database and Approximate Cases
• Faster Algorithms for Privately Releasing Marginals
• Private Learning and Sanitization: Pure vs. Approximate Differential Privacy
• Privately Releasing Conjunctions and the Statistical Query Barrier
• On the geometry of differential privacy
• Interactive privacy via the median mechanism
• The price of privately releasing contingency tables and the spectra of random matrices with correlated rows
• Lower Bounds in Differential Privacy
• Iterative Constructions and Private Data Release
• Characterizing the sample complexity of private learners
• Faster private release of marginals on small databases
• Bounds on the Sample Complexity for Private Learning and Private Data Release
• Differential Privacy and the Fat-Shattering Dimension of Linear Queries
• Our Data, Ourselves: Privacy Via Distributed Noise Generation
• New Efficient Attacks on Statistical Disclosure Control Mechanisms
• Collusion-secure fingerprinting for digital data
• On the complexity of differentially private data release
• Advances in Cryptology – CRYPTO 2004
• Answering n _{2+o(1)} counting queries with differential privacy is hard
• Theory of Cryptography