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Electronic Colloquium on Computational Complexity

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All reports by Author Jan Krajicek:

TR07-007 | 17th January 2007
Jan Krajicek

An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams

We prove an exponential lower bound on the size of proofs
in the proof system operating with ordered binary decision diagrams
introduced by Atserias, Kolaitis and Vardi. In fact, the lower bound
applies to semantic derivations operating with sets defined by OBDDs.
We do not assume ... more >>>

TR04-018 | 24th January 2004
Jan Krajicek

Diagonalization in proof complexity

We study the diagonalization in the context of proof
complexity. We prove that at least one of the
following three conjectures is true:

1. There is a boolean function computable in E
that has circuit complexity $2^{\Omega(n)}$.

2. NP is not closed under the complement.

3. There is no ... more >>>

TR03-055 | 20th July 2003
Jan Krajicek

Implicit proofs

We describe a general method how to construct from
a propositional proof system P a possibly much stronger
proof system iP. The system iP operates with
exponentially long P-proofs described ``implicitly''
by polynomial size circuits.

As an example we prove that proof system iEF, implicit EF,
corresponds to bounded ... more >>>

TR00-033 | 22nd May 2000
Jan Krajicek

Tautologies from pseudo-random generators

Revisions: 1

We consider tautologies formed from a pseudo-random
number generator, defined in Kraj\'{\i}\v{c}ek \cite{Kra99}
and in Alekhnovich et.al. \cite{ABRW}.
We explain a strategy of proving their hardness for EF via
a conjecture about bounded arithmetic formulated
in Kraj\'{\i}\v{c}ek \cite{Kra99}. Further we give a
purely finitary statement, in a ... more >>>

TR97-015 | 21st April 1997
Jan Krajicek

Interpolation by a game

We introduce a notion of a "real game"
(a generalization of the Karchmer - Wigderson game),
and "real communication complexity",
and relate them to the size of monotone real formulas
and circuits. We give an exponential lower bound
for tree-like monotone protocols of small real
communication complexity ... more >>>

TR94-018 | 12th December 1994
Jan Krajicek, Pavel Pudlak, Alan Woods

An Exponential Lower Bound to the Size of Bounded Depth Frege Proofs of the Pigeonhole Principle

We prove lower bounds of the form $exp\left(n^{\epsilon_d}\right),$
$\epsilon_d>0,$ on the length of proofs of an explicit sequence of
tautologies, based on the Pigeonhole Principle, in proof systems
using formulas of depth $d,$ for any constant $d.$ This is the
largest lower bound for the strongest proof system, for which ... more >>>

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