Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with Monotone circuits:
TR96-026 | 25th March 1996
Stasys Jukna

Finite Limits and Monotone Computations

Revisions: 1 , Comments: 1

We prove a general combinatorial lower bound on the
size of monotone circuits. The argument is different from
Razborov's method of approximation, and is based on Sipser's
notion of `finite limit' and Haken's `counting bottlenecks' idea.
We then apply this criterion to the ... more >>>

TR05-021 | 14th February 2005
Stasys Jukna

Disproving the single level conjecture

Revisions: 2 , Comments: 1

We consider the minimal number of AND and OR gates in monotone
circuits for quadratic boolean functions, i.e. disjunctions of
length-$2$ monomials. The single level conjecture claims that
monotone single level circuits, i.e. circuits which have only one
level of AND gates, for quadratic functions ... more >>>

TR15-059 | 10th April 2015
Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

Feasible Interpolation for QBF Resolution Calculi

In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling CDCL or expansion-based solving. This both provides the first general lower bound method for QBF ... more >>>

TR17-042 | 6th March 2017
Pavel Hrubes, Pavel Pudlak

Random formulas, monotone circuits, and interpolation

We prove new lower bounds on the sizes of proofs in the Cutting Plane proof system, using a concept that we call "unsatisfiability certificate". This approach is, essentially, equivalent to the well-known feasible interpolation method, but is applicable to CNF formulas that do not seem suitable for interpolation. Specifically, we ... more >>>

TR17-144 | 27th September 2017
Moritz Müller, Ján Pich

Feasibly constructive proofs of succinct weak circuit lower bounds

Revisions: 1

We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit strings of length $n$. In 1995 Razborov showed that many can be proved in Cook’s theory $PV_1$, a bounded arithmetic formalizing polynomial time reasoning. He formalized circuit lower bound statements for small $n$ of ... more >>>

TR23-086 | 8th June 2023
Dmitry Sokolov

Random $(\log n)$-CNF are Hard for Cutting Planes (Again)

The random $\Delta$-CNF model is one of the most important distribution over $\Delta\text{-}\mathrm{SAT}$ instances. It is closely connected to various areas of computer science, statistical physics, and is a benchmark for satisfiability algorithms. Fleming, Pankratov, Pitassi, and Robere and independently Hrubes and Pudlak showed that when $\Delta = \Theta(\log n)$, ... more >>>

TR23-153 | 19th October 2023
Natalia Dobrokhotova-Maikova, Alexander Kozachinskiy, Vladimir Podolskii

Towards Simpler Sorting Networks and Monotone Circuits for Majority

In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of arity $2$ and the generalized setting with operations of arity $k$, where $k$ is a ... more >>>

ISSN 1433-8092 | Imprint