Logic at Botik'89 Symposium on logical foundations of computer science
On search decision and the efficiency of polynomial-time algorithms
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The history and status of the P versus NP question
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
On the Amount of Nondeterminism and the Power of Verifying
SIAM Journal on Computing
The Shrinkage Exponent of de Morgan Formulas is 2
SIAM Journal on Computing
Separating Nondeterministic Time Complexity Classes
Journal of the ACM (JACM)
Relations Among Complexity Measures
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
SIAM Journal on Computing
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
A Probabilistic-Time Hierarchy Theorem for "Slightly Non-uniform" Algorithms
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
Computations with a restricted number of nondeterministic steps (Extended Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On the complexity of intersecting finite state automata and NL versus NP
Theoretical Computer Science
Comparing Notions of Full Derandomization
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Circuits, cnfs, and satisfiability
Circuits, cnfs, and satisfiability
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Short PCPs Verifiable in Polylogarithmic Time
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Holographic Proofs and Derandomization
SIAM Journal on Computing
Time-space lower bounds for satisfiability
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A Duality between Clause Width and Clause Density for SAT
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
A survey of lower bounds for satisfiability and related problems
Foundations and Trends® in Theoretical Computer Science
An Isomorphism Between Subexponential and Parameterized Complexity Theory
SIAM Journal on Computing
Lower bounds for natural proof systems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Time-Space Tradeoffs for Counting NP Solutions Modulo Integers
Computational Complexity
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
The Complexity of Satisfiability of Small Depth Circuits
Parameterized and Exact Computation
Bounded fixed-parameter tractability and log2n nondeterministic bits
Journal of Computer and System Sciences
Combinatorial PCPs with Efficient Verifiers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
The time complexity of constraint satisfaction
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Improved simulation of nondeterministic turing machines
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
A full derandomization of schöning's k-SAT algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
Nexp does not have non-uniform quasipolynomial-size ACC circuits of o(log log n) depth
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Connecting SAT algorithms and complexity lower bounds
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Satisfiability certificates verifiable in subexponential time
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Robust simulations and significant separations
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Diagonalization strikes back: some recent lower bounds in complexity theory
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Guest column: a casual tour around a circuit complexity bound
ACM SIGACT News
On beating the hybrid argument
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Marginal hitting sets imply super-polynomial lower bounds for permanent
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
A satisfiability algorithm for AC0
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved simulation of nondeterministic Turing machines
Theoretical Computer Science
Finding efficient circuits for ensemble computation
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
On the limits of sparsification
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
European Journal of Combinatorics
Communications of the ACM
Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Natural proofs versus derandomization
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The P vs NP problem arose from the question of whether exhaustive search is necessary for problems with short verifiable solutions. We still do not know if even a slight algorithmic improvement over exhaustive search is universally possible for all NP problems, and to date no major consequences have been derived from the assumption that an improvement exists. We show that there are natural NP and BPP problems for which minor algorithmic improvements over the trivial deterministic simulation already entail lower bounds such as NEXP is not in P/poly and LOGSPACE is not equal to NP. These results are especially interesting given that similar improvements have been found for many other hard problems. Optimistically, one might hope our results suggest a new path to lower bounds; pessimistically, they show that carrying out the seemingly modest program of finding slightly better algorithms for all search problems may be extremely difficult (if not impossible). We also prove unconditional superpolynomial time-space lower bounds for improving on exhaustive search.