A Circuit-Based Proof of Toda's Theorem

@article{Kannan1993ACP,
  title={A Circuit-Based Proof of Toda's Theorem},
  author={Ravi Kannan and H. Venkateswaran and V. Vinay and Andrew Chi-Chih Yao},
  journal={Inf. Comput.},
  year={1993},
  volume={104},
  pages={271-276}
}
Abstract We present a simple proof of Toda′s result (Toda (1989), in "Proceedings, 30th Annual IEEE Symposium on Foundations of Computer Science," pp. 514-519), which states that ⊕ P is hard for the Polynomial Hierarchy under randomized reductions. Our approach is circuit-based in the sense that we start with uniform circuit definitions of the Polynomial Hierarchy and apply the Valiant-Vazirani lemma on these circuits (Valiant and Vazirani (1986), Thoeret. Comput. Sci. 47, 85-93). 

Topics from this paper.

Citations

Publications citing this paper.
SHOWING 1-10 OF 12 CITATIONS