Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Relativized circuit complexity
Journal of Computer and System Sciences
Average case complete problems
SIAM Journal on Computing
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
The monotone circuit complexity of Boolean functions
Combinatorica
The complexity of Boolean functions
The complexity of Boolean functions
The complexity of Boolean networks
The complexity of Boolean networks
Thinking (vol. 3)
Journal of Computer and System Sciences
Kolmogorov complexity and its applications
Handbook of theoretical computer science (vol. A)
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Randomized algorithms
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Selected papers on computer science
Selected papers on computer science
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
SIAM Journal on Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Computational Work and Time on Finite Machines
Journal of the ACM (JACM)
Relations Among Complexity Measures
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Some pointed questions concerning asymptotic lower bounds, and news from the isomorphism front
Current trends in theoretical computer science
The Complexity of Computing
Quantum computation and quantum information
Quantum computation and quantum information
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Structure of complexity in the weak monadic second-order theories of the natural numbers
STOC '74 Proceedings of the sixth 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
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Guest Column: NP-complete problems and physical reality
ACM SIGACT News
Beyond NP: the work and legacy of Larry Stockmeyer
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A note on dimensions of polynomial size circuits
Theoretical Computer Science
Modular Pluggable Analyses for Data Structure Consistency
IEEE Transactions on Software Engineering
Algorithms and theory of computation handbook
Logics for unranked trees: an overview
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the model-checking of monadic second-order formulas with edge set quantifications
Discrete Applied Mathematics
Synthesis for unbounded bit-vector arithmetic
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Linear temporal logic and linear dynamic logic on finite traces
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
| Hi-index | 0.01 |
An exponential lower bound on the circuit complexity of deciding the weak monadic second-order theory of one successor (WS1S) is proved. Circuits are built from binary operations, or 2-input gates, which compute arbitrary Boolean functions. In particular, to decide the truth of logical formulas of length at most 610 in this second-order language requires a circuit containing at least 10125 gates. So even if each gate were the size of a proton, the circuit would not fit in the known universe. This result and its proof, due to both authors, originally appeared in 1974 in the Ph.D. thesis of the first author. In this article, the proof is given, the result is put in historical perspective, and the result is extended to probabilistic circuits.*