Computational Complexity II Course Instructor : V . Arvind Monotone Circuit Lower
نویسنده
چکیده
The holy grail for computer science has been trying to somehow show that P 6= NP . And another problem that is equally intriguing is to show that NP * P/poly, trying to find circuit (over ∧,∨,¬) lower bounds for problems in NP . But suppose we were able to drop the ¬ gate from the basis, we would be able to compute only monotone functions, but can we show some monotone circuit lower bounds for some hard problem in NP? In this lecture we shall see that the CLIQUE function requires super-polynomial sized monotone circuits.
منابع مشابه
On Lower Bounds for Constant Width Arithmetic Circuits
The motivation for this paper is to study the complexity of constant-width arithmetic circuits. Our main results are the following. 1. For every k > 1, we provide an explicit polynomial that can be computed by a linear-sized monotone circuit of width 2k but has no subexponential-sized monotone circuit of width k. It follows, from the definition of the polynomial, that the constant-width and the...
متن کاملIkenmeyer C, Komarath B, Lenzen C, Lysikov V, Mokhov A, Sreenivasaiah K.
The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is polynomially bounded while every hazardfree implementation is provably of exponential size. Previous lower bounds on the hazard-free complexity were only valid for ...
متن کاملMonotone Circuit Lower Bounds from Resolution
For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a gadget-composed version of F is hard to refute in any proof system whose lines are computed by efficient communication protocols—or, equivalently, that a monotone function associated with F has large monotone circuit complexity. Our result extends to monotone real circuits, which yields new...
متن کاملThe Complexity of Two Register and Skew Arithmetic Computation
We study two register arithmetic computation and skew arithmetic circuits. Our main results are the following: • For commutative computations, we show that an exponential circuit size lower bound for a model of 2-register straight-line programs (SLPs) which is a universal model of computation (unlike width-2 algebraic branching programs that are not universal [AW11]). • For noncommutative compu...
متن کاملArithmetic Circuit Size, Identity Testing, and Finite Automata
Let F〈x1, x2, · · · , xn〉 be the noncommutative polynomial ring over a field F, where the xi’s are free noncommuting formal variables. Given a finite automaton A with the xi’s as alphabet, we can define polynomials f(mod A) and f(div A) obtained by natural operations that we call intersecting and quotienting the polynomial f by A. Related to intersection, we also define the Hadamard product f ◦...
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:
دوره شماره
صفحات -
تاریخ انتشار 2006