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Electronic Colloquium on Computational Complexity

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Reports tagged with propositional proof systems:
TR94-015 | 12th December 1994
Miklos Ajtai

Symmetric Systems of Linear Equations modulo $p$

Suppose that $p$ is a prime number $A$ is a finite set
with $n$ elements
and for each sequence $a=<a_{1},...,a_{k}>$ of length $k$ from the
elements of
$A$, $x_{a}$ is a variable. (We may think that $k$ and $p$ are fixed an
$n$ is sufficiently large.) We will ... more >>>

TR97-026 | 18th June 1997
Jochen Me\3ner, Jacobo Toran

Optimal proof systems for Propositional Logic and complete sets

A polynomial time computable function $h:\Sigma^*\to\Sigma^*$ whose range
is the set of tautologies in Propositional Logic (TAUT), is called
a proof system. Cook and Reckhow defined this concept
and in order to compare the relative strenth of different proof systems,
they considered the notion ... more >>>

TR98-021 | 7th April 1998
Shai Ben-David, Anna Gringauze.

On the Existence of Propositional Proof Systems and Oracle-relativized Propositional Logic.

Revisions: 1

We investigate sufficient conditions for the existence of
optimal propositional proof systems (PPS).
We concentrate on conditions of the form CoNF = NF.
We introduce a purely combinatorial property of complexity classes
- the notions of {\em slim} vs. {\em fat} classes.
These notions partition the ... more >>>

TR03-011 | 17th February 2003
Christian Glaßer, Alan L. Selman, Samik Sengupta, Liyu Zhang

Disjoint NP-Pairs

We study the question of whether the class DisNP of
disjoint pairs (A, B) of NP-sets contains a complete pair.
The question relates to the question of whether optimal
proof systems exist, and we relate it to the previously
studied question of whether there exists ... more >>>

TR04-082 | 9th September 2004
Olaf Beyersdorff

Representable Disjoint NP-Pairs

Revisions: 1

We investigate the class of disjoint NP-pairs under different reductions.
The structure of this class is intimately linked to the simulation order
of propositional proof systems, and we make use of the relationship between
propositional proof systems and theories of bounded arithmetic as the main
tool of our analysis.
more >>>

TR04-106 | 19th November 2004
Christian Glaßer, Alan L. Selman, Liyu Zhang

Canonical Disjoint NP-Pairs of Propositional Proof Systems

We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to
the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is
identical. Secondly, we show that this degree structure is not superficial: Assuming there exist ... more >>>

TR05-077 | 15th July 2005
Zenon Sadowski

On a D-N-optimal acceptor for TAUT

The notion of an optimal acceptor for TAUT (the optimality
property is stated only for input strings from TAUT) comes from the line
of research aimed at resolving the question of whether optimal
propositional proof systems exist. In this paper we introduce two new
types of optimal acceptors, a D-N-optimal ... more >>>

TR05-083 | 24th July 2005
Olaf Beyersdorff

Disjoint NP-Pairs from Propositional Proof Systems

For a proof system P we introduce the complexity class DNPP(P)
of all disjoint NP-pairs for which the disjointness of the pair is
efficiently provable in the proof system P.
We exhibit structural properties of proof systems which make the
previously defined canonical NP-pairs of these proof systems hard ... more >>>

TR06-142 | 26th October 2006
Olaf Beyersdorff

On the Deduction Theorem and Complete Disjoint NP-Pairs

In this paper we ask the question whether the extended Frege proof
system EF satisfies a weak version of the deduction theorem. We
prove that if this is the case, then complete disjoint NP-pairs
exist. On the other hand, if EF is an optimal proof system, ... more >>>

TR07-018 | 1st March 2007
Christian Glaßer, Alan L. Selman, Liyu Zhang

The Informational Content of Canonical Disjoint NP-Pairs

We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions.

Q1: Where does the implication [can(f) \le_m can(g) => f \le_s ... more >>>

TR09-092 | 8th October 2009
Olaf Beyersdorff, Johannes Köbler, Sebastian Müller

Proof Systems that Take Advice

One of the starting points of propositional proof complexity is the seminal paper by Cook and Reckhow (JSL 79), where they defined
propositional proof systems as poly-time computable functions which have all propositional tautologies as their range. Motivated by provability consequences in bounded arithmetic, Cook and Krajicek (JSL 07) have ... more >>>

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