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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > OPTIMAL PROOF SYSTEMS:
Reports tagged with Optimal proof systems:
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 >>>


TR05-123 | 25th October 2005
Olaf Beyersdorff

Tuples of Disjoint NP-Sets

Disjoint NP-pairs are a well studied complexity theoretic concept with
important applications in cryptography and propositional proof
complexity.

In this paper we introduce a natural generalization of the notion of
disjoint NP-pairs to disjoint k-tuples of NP-sets for k>1.
We define subclasses of ... more >>>


TR08-107 | 12th November 2008
Zenon Sadowski

Optimal Proof Systems and Complete Languages

We investigate the connection between optimal propositional
proof systems and complete languages for promise classes.
We prove that an optimal propositional proof system exists
if and only if there exists a propositional proof system
in which every promise class with the test set in co-NP
... more >>>


TR09-081 | 27th August 2009
Olaf Beyersdorff, Zenon Sadowski

Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes

In this paper we investigate the following two questions:

Q1: Do there exist optimal proof systems for a given language L?
Q2: Do there exist complete problems for a given promise class C?

For concrete languages L (such as TAUT or SAT and concrete promise classes C (such as NP ... more >>>


TR18-178 | 9th October 2018
Leroy Chew

Hardness and Optimality in QBF Proof Systems Modulo NP

Quantified Boolean Formulas (QBFs) extend propositional formulas with Boolean quantifiers. Working with QBF differs from propositional logic in its quantifier handling, but as propositional satisfiability (SAT) is a subproblem of QBF, all SAT hardness in solving and proof complexity transfers to QBF. This makes it difficult to analyse efforts dealing ... more >>>




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