On the Complexity of Bilinear Forms

This paper provides some new lower and upper bounds on computing bilinear forms by arithmetic circuits. The complexity measures considered are circuit size, formula size and time-space trade-offs.

[1]  Jacques Morgenstern,et al.  Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform , 1973, JACM.

[2]  Aravind Srinivasan,et al.  Computing with very weak random sources , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[3]  Leslie G. Valiant,et al.  Graph-Theoretic Properties in computational Complexity , 1976, J. Comput. Syst. Sci..

[4]  Martin Tompa Time-Space Tradeoffs for Computing Functions, Using Connectivity Properties of Their Circuits , 1980, J. Comput. Syst. Sci..

[5]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[6]  Avi Wigderson,et al.  Superconcentrators, generalizers and generalized connectors with limited depth , 1983, STOC.

[7]  Nicholas Pippenger,et al.  Superconcentrators of Depth 2 , 1982, J. Comput. Syst. Sci..

[8]  Martin Tompa,et al.  Time-space tradeoffs for computing functions, using connectivity properties of their circuits , 1978, J. Comput. Syst. Sci..

[9]  Noga Alon,et al.  Meanders and Their Applications in Lower Bounds Arguments , 1988, J. Comput. Syst. Sci..

[10]  V. Strassen Die Berechnungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoeffizienten , 1973 .

[11]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[12]  MorgensternJacques How to compute fast a function and all its derivatives , 1985 .

[13]  Bernard Chazelle A spectral approach to lower bounds , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[14]  Avi Wigderson,et al.  Expanders That Beat the Eigenvalue Bound: Explicit Construction and Applications , 1999, Comb..