A Criterion for Monotone Circuit Complexity

نویسنده

  • Stasys Jukna
چکیده

In this paper we study the lower bounds problem for monotone circuits. The main goal is to extend and simplify the well known method of approximations proposed by A. Razborov in 1985. The main result is the following combi-natorial criterion for the monotone circuit complexity: a monotone Boolean

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Monotone 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 کامل

Ikenmeyer 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 کامل

Computational Complexity II Course Instructor : V . Arvind Monotone Circuit Lower

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 ...

متن کامل

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 کامل

Finite Limits and Monotone Computations: The Lower Bounds Criterion

Our main result is a combinatorial lower bounds criterion for monotone circuits over the reals. We allow any unbounded fanin non-decreasing real-valued functions as gates. The only requirement is their "local-ity". Unbounded fanin AND and OR gates, as well as any threshold gate T m s (x 1 ; : : : ; x m) with small enough threshold value minfs; m ? s + 1g, are simplest examples of local gates. T...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1991