The Power of Diversity
In computations realized by finite automata, a rich understanding has come from comparing the algebraic structure of the machines to the combinatorics of the languages being recognized. In this expository paper, we will first survey some basic ideas that have been useful in this model. In the second part, we sketch how this dual approach can be generalized to study some important class of boolean circuits, what results have been obtained, what questions are still open. The intuition gained in the simple model sometimes carry through, sometimes not, so that one has to be careful on what conjectures to make.
KeywordsSolvable Group Wreath Product Regular Language Boolean Circuit Output Gate
Unable to display preview. Download preview PDF.
- 13.Sipser, M.: Borel sets and circuit complexity. In: Proceedings of the Fifteenth Annual ACM Symposium on the Theory of Computing, pp. 61–69 (1983)Google Scholar
- 15.Thérien, D.: Classification of finite monoids: The language approach. In: Theoretical Computer Science, vol. 14, pp. 195–208 (1981)Google Scholar