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Electronic Colloquium on Computational Complexity

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All reports by Author Ján Pich:

TR18-158 | 11th September 2018
Igor Carboni Oliveira, Ján Pich, Rahul Santhanam

Hardness magnification near state-of-the-art lower bounds

Revisions: 1

This work continues the development of hardness magnification. The latter proposes a strategy for showing strong complexity lower bounds by reducing them to a refined analysis of weaker models, where combinatorial techniques might be successful.

We consider gap versions of the meta-computational problems MKtP and MCSP, where one needs ... more >>>

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

Feasibly constructive proofs of succinct weak circuit lower bounds

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 >>>

TR17-044 | 21st February 2017
Olaf Beyersdorff, Luke Hinde, Ján Pich

Reasons for Hardness in QBF Proof Systems

Revisions: 1

We aim to understand inherent reasons for lower bounds for QBF proof systems and revisit and compare two previous approaches in this direction.

The first of these relates size lower bounds for strong QBF Frege systems to circuit lower bounds via strategy extraction (Beyersdorff & Pich, LICS'16). Here we ... more >>>

TR16-011 | 27th January 2016
Olaf Beyersdorff, Ján Pich

Understanding Gentzen and Frege systems for QBF

Recently Beyersdorff, Bonacina, and Chew (ITCS'16) introduced a natural class of Frege systems for quantified Boolean formulas (QBF) and showed strong lower bounds for restricted versions of these systems. Here we provide a comprehensive analysis of the new extended Frege system from Beyersdorff et al., denoted EF+$\forall$red, which is a ... more >>>

TR13-077 | 14th May 2013
Ján Pich

Circuit Lower Bounds in Bounded Arithmetics

We prove that $T_{NC^1}$, the true universal first-order theory in the language containing names for all uniform $NC^1$ algorithms, cannot prove that for sufficiently large $n$, SAT is not computable by circuits of size $n^{2kc}$ where $k\geq 1, c\geq 4$ unless each function $f\in SIZE(n^k)$ can be approximated by formulas ... more >>>

TR10-046 | 22nd March 2010
Ján Pich

Nisan-Wigderson generators in proof systems with forms of interpolation

We prove that the Nisan-Wigderson generators based on computationally hard functions and suitable matrices are hard for propositional proof systems that admit feasible interpolation.

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