All reports by Author Robert Robere:

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TR22-058
| 26th April 2022
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Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao#### Separations in Proof Complexity and TFNP

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TR22-018
| 15th February 2022
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Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao#### Further Collapses in TFNP

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TR22-003
| 4th January 2022
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Noah Fleming, Stefan Grosser, Mika Göös, Robert Robere#### On Semi-Algebraic Proofs and Algorithms

Revisions: 1

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TR21-170
| 25th November 2021
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Reyad Abed Elrazik, Robert Robere, Assaf Schuster, Gal Yehuda#### Pseudorandom Self-Reductions for NP-Complete Problems

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TR21-158
| 12th November 2021
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Noah Fleming, Toniann Pitassi, Robert Robere#### Extremely Deep Proofs

Revisions: 1

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TR21-035
| 13th March 2021
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Robert Robere, Jeroen Zuiddam#### Amortized Circuit Complexity, Formal Complexity Measures, and Catalytic Algorithms

Revisions: 1

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TR19-128
| 24th September 2019
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Anna Gal, Robert Robere#### Lower Bounds for (Non-monotone) Comparator Circuits

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TR18-163
| 18th September 2018
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Mika Göös, Pritish Kamath, Robert Robere, Dmitry Sokolov#### Adventures in Monotone Complexity and TFNP

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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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TR17-045
| 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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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

Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao

It is well-known that Resolution proofs can be efficiently simulated by Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to exploit huge coefficients: Resolution cannot be efficiently simulated by SA when the coefficients are written in unary. We also show that Reversible Resolution (a variant of MaxSAT ... more >>>

Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao

We show $\text{EOPL}=\text{PLS}\cap\text{PPAD}$. Here the class $\text{EOPL}$ consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubacek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result yields a new simpler proof of the breakthrough collapse ... more >>>

Noah Fleming, Stefan Grosser, Mika Göös, Robert Robere

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 >>>

Reyad Abed Elrazik, Robert Robere, Assaf Schuster, Gal Yehuda

A language $L$ is random-self-reducible if deciding membership in $L$ can be reduced (in polynomial time) to deciding membership in $L$ for uniformly random instances. It is known that several "number theoretic" languages (such as computing the permanent of a matrix) admit random self-reductions. Feigenbaum and Fortnow showed that NP-complete ... more >>>

Noah Fleming, Toniann Pitassi, Robert Robere

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 >>>

Robert Robere, Jeroen Zuiddam

We study the amortized circuit complexity of boolean functions.

Given a circuit model $\mathcal{F}$ and a boolean function $f : \{0,1\}^n \rightarrow \{0,1\}$, the $\mathcal{F}$-amortized circuit complexity is defined to be the size of the smallest circuit that outputs $m$ copies of $f$ (evaluated on the same input), ...
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Anna Gal, Robert Robere

Comparator circuits are a natural circuit model for studying the concept of bounded fan-out computations, which intuitively corresponds to whether or not a computational model can make "copies" of intermediate computational steps. Comparator circuits are believed to be weaker than general Boolean circuits, but they can simulate Branching Programs and ... more >>>

Mika Göös, Pritish Kamath, Robert Robere, Dmitry Sokolov

$\mathbf{Separations:}$ We introduce a monotone variant of XOR-SAT and show it has exponential monotone circuit complexity. Since XOR-SAT is in NC^2, this improves qualitatively on the monotone vs. non-monotone separation of Tardos (1988). We also show that monotone span programs over R can be exponentially more powerful than over finite ... 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 ...
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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 ...
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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 >>>