All reports by Author Toniann Pitassi:

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TR19-106
| 12th August 2019
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Noah Fleming, Pravesh Kothari, Toniann Pitassi#### Semialgebraic Proofs and Efficient Algorithm Design

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TR19-103
| 7th August 2019
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Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi#### Query-to-Communication Lifting Using Low-Discrepancy Gadgets

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TR19-043
| 12th March 2019
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Toniann Pitassi, Morgan Shirley, Thomas Watson#### Nondeterministic and Randomized Boolean Hierarchies in Communication Complexity

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TR19-024
| 20th February 2019
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Russell Impagliazzo, Sasank Mouli, Toniann Pitassi#### The Surprising Power of Constant Depth Algebraic Proofs

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TR17-165
| 3rd November 2017
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Toniann Pitassi, Robert Robere#### Lifting Nullstellensatz to Monotone Span Programs over Any Field

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

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TR17-053
| 22nd March 2017
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Mika Göös, Toniann Pitassi, Thomas Watson#### Query-to-Communication Lifting for BPP

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TR17-045
| 7th March 2017
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Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere#### Random CNFs are Hard for Cutting Planes

Revisions: 2

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TR17-024
| 16th February 2017
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Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson#### Query-to-Communication Lifting for P^NP

Revisions: 1

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TR16-188
| 21st November 2016
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Toniann Pitassi, Robert Robere#### Strongly Exponential Lower Bounds for Monotone Computation

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TR16-101
| 1st July 2016
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Toniann Pitassi, Iddo Tzameret#### Algebraic Proof Complexity: Progress, Frontiers and Challenges

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TR16-064
| 19th April 2016
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Stephen A. Cook, Toniann Pitassi, Robert Robere, Benjamin Rossman#### Exponential Lower Bounds for Monotone Span Programs

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TR15-169
| 23rd October 2015
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Mika Göös, T.S. Jayram, Toniann Pitassi, Thomas Watson#### Randomized Communication vs. Partition Number

Revisions: 1

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TR15-050
| 4th April 2015
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Mika Göös, Toniann Pitassi, Thomas Watson#### Deterministic Communication vs. Partition Number

Revisions: 1

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TR15-049
| 3rd April 2015
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Mika Göös, Toniann Pitassi, Thomas Watson#### The Landscape of Communication Complexity Classes

Revisions: 1

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TR14-078
| 7th June 2014
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Mika Göös, Toniann Pitassi, Thomas Watson#### Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication

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TR14-052
| 14th April 2014
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Joshua Grochow, Toniann Pitassi#### Circuit complexity, proof complexity, and polynomial identity testing

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TR13-054
| 4th April 2013
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Yuval Filmus, Toniann Pitassi, Robert Robere, Stephen A. Cook#### Average Case Lower Bounds for Monotone Switching Networks

Revisions: 1

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TR11-106
| 6th August 2011
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Andrew McGregor, Ilya Mironov, Toniann Pitassi, Omer Reingold, Kunal Talwar, Salil Vadhan#### The Limits of Two-Party Differential Privacy

Noah Fleming, Pravesh Kothari, Toniann Pitassi

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 >>>

Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi

Lifting theorems are theorems that relate the query complexity of a function $f:\left\{ 0,1 \right\}^n\to \left\{ 0,1 \right\}$ to the communication complexity of the composed function $f\circ g^n$, for some “gadget” $g:\left\{ 0,1 \right\}^b\times \left\{ 0,1 \right\}^b\to \left\{ 0,1 \right\}$. Such theorems allow transferring lower bounds from query complexity to ... more >>>

Toniann Pitassi, Morgan Shirley, Thomas Watson

We study the Boolean Hierarchy in the context of two-party communication complexity, as well as the analogous hierarchy defined with one-sided error randomness instead of nondeterminism. Our results provide a complete picture of the relationships among complexity classes within and across these two hierarchies. In particular, we prove a query-to-communication ... more >>>

Russell Impagliazzo, Sasank Mouli, Toniann Pitassi

A major open problem in proof complexity is to prove super-polynomial lower bounds for AC^0[p]-Frege proofs. This system is the analog of AC^0[p], the class of bounded depth circuits with prime modular counting gates. Despite strong lower bounds for this class dating back thirty years (Razborov, '86 and Smolensky, '87), ... more >>>

Toniann Pitassi, Robert Robere

We characterize the size of monotone span programs computing certain "structured" boolean functions by the Nullstellensatz degree of a related unsatisfiable Boolean formula.

This yields the first exponential lower bounds for monotone span programs over arbitrary fields, the first exponential separations between monotone span programs over fields of different ... more >>>

Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere

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 >>>

Mika Göös, Toniann Pitassi, Thomas Watson

For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In particular, this means that many query complexity separations involving randomized models (e.g., classical vs.\ ... more >>>

Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere

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 >>>

Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson

We prove that the $\text{P}^{\small\text{NP}}$-type query complexity (alternatively, decision list width) of any boolean function $f$ is quadratically related to the $\text{P}^{\small\text{NP}}$-type communication complexity of a lifted version of $f$. As an application, we show that a certain "product" lower bound method of Impagliazzo and Williams (CCC 2010) fails to ... more >>>

Toniann Pitassi, Robert Robere

For a universal constant $\alpha > 0$, we prove size lower bounds of $2^{\alpha N}$ for computing an explicit monotone function in NP in the following models of computation: monotone formulas, monotone switching networks, monotone span programs, and monotone comparator circuits, where $N$ is the number of variables of the ... more >>>

Toniann Pitassi, Iddo Tzameret

We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to old problems, and new directions of research. In particular, we focus on tight ... more >>>

Stephen A. Cook, Toniann Pitassi, Robert Robere, Benjamin Rossman

Monotone span programs are a linear-algebraic model of computation which were introduced by Karchmer and Wigderson in 1993. They are known to be equivalent to linear secret sharing schemes, and have various applications in complexity theory and cryptography. Lower bounds for monotone span programs have been difficult to obtain because ... more >>>

Mika Göös, T.S. Jayram, Toniann Pitassi, Thomas Watson

We show that \emph{randomized} communication complexity can be superlogarithmic in the partition number of the associated communication matrix, and we obtain near-optimal \emph{randomized} lower bounds for the Clique vs.\ Independent Set problem. These results strengthen the deterministic lower bounds obtained in prior work (G\"o\"os, Pitassi, and Watson, {\small FOCS~2015}).

more >>>Mika Göös, Toniann Pitassi, Thomas Watson

We show that deterministic communication complexity can be superlogarithmic in the partition number of the associated communication matrix. We also obtain near-optimal deterministic lower bounds for the Clique vs. Independent Set problem, which in particular yields new lower bounds for the log-rank conjecture. All these results follow from a simple ... more >>>

Mika Göös, Toniann Pitassi, Thomas Watson

We prove several results which, together with prior work, provide a nearly-complete picture of the relationships among classical communication complexity classes between $P$ and $PSPACE$, short of proving lower bounds against classes for which no explicit lower bounds were already known. Our article also serves as an up-to-date survey on ... more >>>

Mika Göös, Toniann Pitassi, Thomas Watson

We study whether information complexity can be used to attack the long-standing open problem of proving lower bounds against Arthur--Merlin (AM) communication protocols. Our starting point is to show that---in contrast to plain randomized communication complexity---every boolean function admits an AM communication protocol where on each yes-input, the distribution of ... more >>>

Joshua Grochow, Toniann Pitassi

We introduce a new and very natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomial-size algebraic circuits ($VNP \neq VP$). As a ... more >>>

Yuval Filmus, Toniann Pitassi, Robert Robere, Stephen A. Cook

An approximate computation of a Boolean function by a circuit or switching network is a computation which computes the function correctly on the majority of the inputs (rather than on all inputs). Besides being interesting in their own right, lower bounds for approximate computation have proved useful in many subareas ... more >>>

Andrew McGregor, Ilya Mironov, Toniann Pitassi, Omer Reingold, Kunal Talwar, Salil Vadhan

We study differential privacy in a distributed setting where two parties would like to perform analysis of their joint data while preserving privacy for both datasets. Our results imply almost tight lower bounds on the accuracy of such data analyses, both for specific natural functions (such as Hamming distance) and ... more >>>