Some consequences of our failure to prove non-linear lower bounds on explicit functions

Investigates the consequences of assuming that no explicit function has non-polynomial size Boolean circuit complexity. There are many consequences of this assumption. For example, it immediately proves that P does not equal NP. It also has ramifications for the length of certain interactive proofs.<<ETX>>

[1]  Ingo Wegener,et al.  The complexity of Boolean functions , 1987 .

[2]  D. Ulig On the synthesis of self-correcting schemes from functional elements with a small number of reliable elements , 1974 .

[3]  Wolfgang J. Paul Realizing Boolean Functions on Disjoint sets of Variables , 1976, Theor. Comput. Sci..

[4]  Ravi Kannan,et al.  Circuit-Size Lower Bounds and Non-Reducibility to Sparse Sets , 1982, Inf. Control..

[5]  Carsten Lund,et al.  Efficient probabilistically checkable proofs and applications to approximations , 1993, STOC.

[6]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[7]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[8]  Carsten Lund,et al.  Non-deterministic exponential time has two-prover interactive protocols , 2005, computational complexity.

[9]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[10]  Claude E. Shannon,et al.  The synthesis of two-terminal switching circuits , 1949, Bell Syst. Tech. J..

[11]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[12]  Leonid A. Levin,et al.  Checking computations in polylogarithmic time , 1991, STOC '91.

[13]  Carsten Lund,et al.  Nondeterministic exponential time has two-prover interactive protocols , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[14]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.