Polynomial Hierarchy, Betti Numbers, and a Real Analogue of Toda’s Theorem

The polynomial-time hierarchy

Larry J. Stockmeyer · Theoretical Computer Science · 1976 · 1.3K citations

Complexity and real computation

Choice Reviews Online · 1998 · 1.3K citations

Computing, Computer Science, Mathematics +17

On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines

Lenore Blum, M. Shub, Steve Smale · Bulletin of the American Mathematical Society · 1989 · 1.1K citations · Full text

Computing, Computer Science, Mathematics +17

PP is as Hard as the Polynomial-Time Hierarchy

Seinosuke Toda · SIAM Journal on Computing · 1991 · 677 citations

Computing, Computer Science, Mathematics +17

NP is as easy as detecting unique solutions

Leslie G. Valiant, Vijay V. Vazirani · Theoretical Computer Science · 1986 · 659 citations

Computing, Computer Science, Artificial Intelligence +4