Relating Polynomial Time to Constant Depth

Going back to the seminal paper of Furst, Saxe, and Sipser (1984), analogues between polynomial time classes and constant depth circuit classes have been considered in a number of papers. Oracles separating polynomial time classes have been obtained by diagonalization making essential use of lower bounds for circuit classes. In this note we show how separating oracles can be obtained uniformly from circuit lower bounds without the need of carrying out a particular diagonalization. Our technical tool is the leaf language approach to the definition of complexity classes.

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