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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > NOAH FLEMING:
All reports by Author Noah Fleming:

TR22-051 | 18th April 2022
Vipul Arora, Arnab Bhattacharyya, Noah Fleming, Esty Kelman, Yuichi Yoshida

Low Degree Testing over the Reals

We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the distribution-free testing model. Here, the distance between functions is measured with respect to an unknown distribution $\mathcal{D}$ over $\mathbb{R}^n$ from which we can draw samples. In contrast ... more >>>


TR22-003 | 4th January 2022
Noah Fleming, Stefan Grosser, Mika Göös, Robert Robere

On Semi-Algebraic Proofs and Algorithms

Revisions: 1

We give a new characterization of the Sherali-Adams proof system, showing that there is a degree-$d$ Sherali-Adams refutation of an unsatisfiable CNF formula $C$ if and only if there is an $\varepsilon > 0$ and a degree-$d$ conical junta $J$ such that $viol_C(x) - \varepsilon = J$, where $viol_C(x)$ counts ... more >>>


TR21-158 | 12th November 2021
Noah Fleming, Toniann Pitassi, Robert Robere

Extremely Deep Proofs

Revisions: 1

We further the study of supercritical tradeoffs in proof and circuit complexity, which is a type of tradeoff between complexity parameters where restricting one complexity parameter forces another to exceed its worst-case upper bound. In particular, we prove a new family of supercritical tradeoffs between depth and size for Resolution, ... more >>>


TR21-061 | 29th April 2021
Noah Fleming, Toniann Pitassi

Reflections on Proof Complexity and Counting Principles

This paper surveys the development of propositional proof complexity and the seminal contributions of Alasdair Urquhart. We focus on the central role of counting principles, and in particular Tseitin's graph tautologies, to most of the key advances in lower bounds in proof complexity. We reflect on a couple of key ... more >>>


TR21-012 | 9th February 2021
Noah Fleming, Mika Göös, Russell Impagliazzo, Toniann Pitassi, Robert Robere, Li-Yang Tan, Avi Wigderson

On the Power and Limitations of Branch and Cut

Revisions: 1

The Stabbing Planes proof system was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formulas -- certain unsatisfiable systems of linear equations mod 2 -- which are canonical ... more >>>


TR19-106 | 12th August 2019
Noah Fleming, Pravesh Kothari, Toniann Pitassi

Semialgebraic Proofs and Efficient Algorithm Design

Revisions: 5

Over the last twenty years, an exciting interplay has emerged between proof systems and algorithms. Some natural families of algorithms can be viewed as a generic translation from a proof that a solution exists into an algorithm for finding the solution itself. This connection has perhaps been the most consequential ... more >>>


TR17-151 | 8th October 2017
Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere

Stabbing Planes

We introduce and develop a new semi-algebraic proof system, called Stabbing Planes that is in the style of DPLL-based modern SAT solvers. As with DPLL, there is only one rule: the current polytope can be subdivided by
branching on an inequality and its "integer negation.'' That is, we can (nondeterministically ... more >>>


TR17-045 | 7th March 2017
Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere

Random CNFs are Hard for Cutting Planes

Revisions: 2

The random k-SAT model is the most important and well-studied distribution over
k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for
satisfiablity algorithms, and lastly average-case hardness over this distribution has also
been linked to hardness of approximation via Feige’s hypothesis. In this ... more >>>




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