Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On randomized one-round communication complexity
Computational Complexity
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Information Theory Methods in Communication Complexity
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Polynomial Degree vs. Quantum Query Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
The Quantum Adversary Method and Classical Formula Size Lower Bounds
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
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In this paper, we survey a few recent applications of Kolmogorov complexity to lower bounds in several models of computation. We consider KI complexity of Boolean functions, which gives the complexity of finding a bit where inputs differ, for pairs of inputs that map to different function values. This measure and variants thereof were shown to imply lower bounds for quantum and randomized decision tree complexity (or query complexity) [LM04]. We give a similar result for deterministic decision trees as well. It was later shown in [LLS05] that KI complexity gives lower bounds for circuit depth. We review those results here, emphasizing simple proofs using Kolmogorov complexity, instead of strongest possible lower bounds. We also present a Kolmogorov complexity alternative to Yao's min-max principle [LL04]. As an example, this is applied to randomized one-way communication complexity.