Relating Polynomial Time to Constant Depth
نویسنده
چکیده
Going back to the seminal paper [FSS84] by Furst, Saxe, and Sipser, 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.
منابع مشابه
Lower Bounds for a Proof System with an Expentential Speed-up over Constant-Depth Frege Systems and over Polynomial Calculus
We prove lower bounds for a proof system having exponential speed-up over both polynomial calculus and constant-depth Frege systems in DeMorgan language.
متن کاملOn Proving Circuit Lower Bounds Against PH and Some Related Lower Bounds for Constant Depth Circuits
We consider the problem of proving circuit lower bounds against the polynomial-time hierarchy. We give both positive and negative results. For the positive side, for any fixed integer k > 0, we give an explicit Σp2 language, acceptable by a Σ p 2-machine with running time O(n k2+k), that requires circuit size > nk. This provides a constructive version of an existence theorem of Kannan [Kan82]. ...
متن کاملTR - C 167 title : On Proving Circuit Lower Bounds Against the Polynomial - time Hierarchy : Positive / Negative Results and Some Related Lower Bounds for Constant Depth Circuits
We consider the problem of proving circuit lower bounds against the polynomialtime hierarchy. We give both positive and negative results. For the positive side, for any fixed integer k > 0, we give an explicit Σp2 language, acceptable by a Σ p 2-machine with running time O(nk 2+k), that requires circuit size > nk. This provides a constructive version of an existence theorem of Kannan [Kan82]. O...
متن کاملLower Bounds for Uniform Constant Depth Circuits by Vivek Kashinath Gore
OF THE DISSERTATION Lower Bounds for Uniform Constant Depth Circuits by Vivek Kashinath Gore, Ph.D. Dissertation Director: Professor Eric Allender Boolean circuits were introduced in complexity theory to provide a model for parallel computation. A big advantage of studying Boolean circuits is that they can be viewed as simple combinatorial objects and thus allow us to use many algebraic and com...
متن کاملBounds on the Power of Constant-Depth Quantum Circuits
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, for 0 < ≤ δ ≤ 1, we define BQNC ,δ to be the class of languages recognized by constant depth, polynomial-size quantum circuits with acceptance probability either < (for rejection) or ≥ δ (for a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 207 شماره
صفحات -
تاریخ انتشار 1998