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Electronic Colloquium on Computational Complexity

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All reports by Author Sam Buss:

TR22-141 | 20th October 2022
Sam Buss, Noah Fleming, Russell Impagliazzo

TFNP Characterizations of Proof Systems and Monotone Circuits

Revisions: 2

Connections between proof complexity and circuit complexity have become major tools for obtaining lower bounds in both areas. These connections -- which take the form of interpolation theorems and query-to-communication lifting theorems -- translate efficient proofs into small circuits, and vice versa, allowing tools from one area to be applied ... more >>>

TR20-073 | 5th May 2020
Sam Buss, Dmitry Itsykson, Alexander Knop, Artur Riazanov, Dmitry Sokolov

Lower Bounds on OBDD Proofs with Several Orders

This paper is motivated by seeking lower bounds on OBDD($\land$, weakening, reordering) refutations, namely OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1-NBP($\land$) refutations based on read-once nondeterministic branching programs. These generalize OBDD($\land$, reordering) refutations. There are polynomial size 1-NBP($\land$) refutations of the pigeonhole principle, hence ... more >>>

TR18-041 | 26th February 2018
Sam Buss, Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

Reordering Rule Makes OBDD Proof Systems Stronger

Atserias, Kolaitis, and Vardi [AKV04] showed that the proof system of Ordered Binary Decision Diagrams with conjunction and weakening, OBDD($\land$, weakening), simulates CP* (Cutting Planes with unary coefficients). We show that OBDD($\land$, weakening) can give exponentially shorter proofs than dag-like cutting planes. This is proved by showing that the Clique-Coloring ... more >>>

TR16-144 | 15th September 2016
Sam Buss, Valentine Kabanets, Antonina Kolokolova, Michal Koucky

Expander Construction in VNC${}^1$

Revisions: 2

We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [Annals of Mathematics, 2002], and show that this analysis can be formalized in the bounded-arithmetic system $VNC^1$ (corresponding to the ``$NC^1$ reasoning''). As a corollary, we prove the ... more >>>

TR15-163 | 11th October 2015
James Aisenberg, Maria Luisa Bonet, Sam Buss

2-D Tucker is PPA complete

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for $k$-D Tucker for all $k\ge 2$. This corrects a claim in the literature that the Tucker search problem is in PPAD.

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TR11-031 | 8th March 2011
Sam Buss, Ryan Williams

Limits on Alternation-Trading Proofs for Time-Space Lower Bounds

This paper characterizes alternation trading based proofs that satisfiability is not in the time and space bounded class $\DTISP(n^c, n^\epsilon)$, for various values $c<2$ and $\epsilon<1$. We characterize exactly what can be proved in the $\epsilon=0$ case with currently known methods, and prove the conjecture of Williams that $c=2\cos(\pi/7)$ is ... more >>>

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