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Re: P=NP Proof Published at CERN
Posted:
May 10, 2009 4:58 PM
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8XPM9-7F9HD-4JJQP-TP64Y-RPFFV
762HW-QD98X-TQVXJ-8RKRQ-RJC9V
I Just Proved [P=NP] and I get to announce it on
Usenet.
Source: http://coding.derkeiler.com/Archive/General/comp.theory/200904/msg00122.html
From: Martin Michael Musatov <marty.musatov@xxxxxxxxx>·
Date: Sun, 26 Apr 2009 07:35:05 0700 (PDT)·
http://ar.wikipedia.org/wiki/FB'4_'DE3*./E:9DJ_'D('4'_2
'D1,'! 'DE4'1C) AJ 'D*5HJ* D*/J/ E3*B(D 41H7 BHB 'DF41 AJ E4'1J9
HJCJEJ/J' (JF*GJ 'D*5HJ* AJ 3 E'JH 2009). 5H* 'D"F!
7D('* 'D5HD 9DI 'DEF 'D/1'3J) DHJCJE'FJ' 2009 EA*H) 'D"F 3,D 'D"F
[#:DB]
[3'9/F' AJ 'D*1,E)!]
F/9HC DDE3'GE) AJ #3(H9 'D*'1J. 'D93C1J HGH #/ 'D#3'(J9 'DE*9//) EF
#3'(J9 'DHJCJ.
[#:DB]
FB'4 'DE3*./E:9DJ 'D('4' 2
EF HJCJ(J/J' 'DEH3H9) 'D1)
*H,/ D/JC 13'&D ,/J/) (".1 *:JJ1).
Date: 1 Apr 2004 10:30:59 0800
Making use of a new type of modeltheoretic tool the Boolean Sieve
we have been able to construct a Ptime algorithm for SAT, thus
providing a resolution to one of the most famous, longstanding open
problems of Theoretical Computer Science. A detailed, but accessible
and informal, general overview of the Boolean Sieve method (more
information can be found here by carrying out a Google groups search
under "Boolean Sieve" and "Mathematician's Algorithm"). However, a
brief description will be provided below of the method, some
applications outside the specific context of SAT, as well as an
overview of how it was applied to SAT. Opportunity providing, an
abstract or possibly even an online copy of the submitted paper (just
accepted for publication) will be made available at the above Web
site.
What is a Boolean Sieve? Basically, it is a construct that is
generated from a set of models, for an axiomfree theory ("free
theory"), that are defined to filter out the possible logical
relations between a set of statements which could be rendered in that
theory. A possible application may be to seek out significant
axiomatizations that may be applied to the set of operations and
predicates in the underlying free theory. The term "filter" is more
than appropriate given the nature of the formal machinery behind the
method.
For instance, consider Group Theory. An interesting (but not well
known) fact is that groups can be defined by their inverse operation
I Just Proved [P=NP] and I get to announce it on Usenet.
I Just Proved [P=NP] and I get to announce it on Usenet.1
(division), just as well by multiplication. The underlying free theory
is an algebraic sort with the following set of operations:
() |> 1 (identity)
(a, b) |> a/b (quotient)
So, it then becomes natural to ask: what are the logical relations
between the possible statements that could be made over the underlying
free theory. Such a situation is precisely the kind of circumstance
where one would use the Boolean Sieve method.
What one does is write down a bunch of statements (ideally, including
a set of statements that we already know from prior considerations
would completely characterize a group), and then select a bunch of
models for the free theory (which in the case at hand may or may not
actually be groups). Each model should have the property that each
statement has a truth value whose evaluation in that model can be done
"efficiently".
The result is a set of raw data from which a profile can be assembled.
The method of integrating all the basic facts is the Boolean Sieve,
itself. The result of applying the Sieve is an efficient
characterization, as a set of Horn clauses, of the Boolean lattice
generated by the statements. >From there (for instance) one could read
off the significant relations and possible axiomatizations, e.g.,
(a/c)/(b/c) = a/b; a/a = 1; a/1 = a
or for Abelien groups:
a(bc) = c(ba); a(ab) = b; 11 = 1.
More generally, a Boolean Sieve will allow us to filter out the
possible relations between a set of statements. The Sieve is called
Complete for that set, if all possible relations are constructed by
the Sieve. What we've actually done is resolve a generalization of SAT
(i.e., determine the validity of a Horn clause involving Boolean
formulas over Nvariables) by defining a process (that is N^3 in
complexity) that generates a complete Boolean Sieve that is N^3 in
size.
Why N^3? Well, this is where it gets interesting: the method for
generating the complete Boolean Sieve is essentially a disguised
version of the Earley parsing algorithm for contextfree grammars! The
significance and nature of this link remains a total mystery to us.
Currently, we are investigating extensions of the Boolean Sieve which
will provide a basis for modeltheoretic theorem proving methods or
"Semantic Theorem Proving". As any expert mathematician will be able
to relate, such an appropach has a far more direct bearing on the way
mathematicians actually approach problems. They will take a stock set
of examples, run a set of possible statements through the examples
(oftentimes subconsciously) and "magically" arrive at a set of
conjectures. We conjecture that the latent method behind this process
is none other than the Boolean Sieve, itself. We even speculate that
"mathematical intuition", itself, may be nothing more than the by
product of this subconscious process. Thus, for instance, one could
develop a more honed "intuition" by having a larger stock of ready
made examples "under the belt", so to say.
Needless to say, these developments will go far beyond the specifics
of the P = NP problem, as most anyone would have been able to
I Just Proved [P=NP] and I get to announce it on Usenet.
I Just Proved [P=NP] and I get to announce it on Usenet.2
> On 9 May, 09:18, Martin Musatov
> <marty.musa...@gmail.com> wrote:
> > An informal and highly experimental, unorthadox
> proof
>
> Does that mean "bogus"?
>
> > P=NP has been
> > published on CERN preprints.
8XPM9-7F9HD-4JJQP-TP64Y-RPFFV
762HW-QD98X-TQVXJ-8RKRQ-RJC9V
I Just Proved [P=NP] and I get to announce it on
Usenet.
Source: http://coding.derkeiler.com/Archive/General/comp.theory/200904/msg00122.html
From: Martin Michael Musatov <marty.musatov@xxxxxxxxx>·
Date: Sun, 26 Apr 2009 07:35:05 0700 (PDT)·
http://ar.wikipedia.org/wiki/FB'4_'DE3*./E:9DJ_'D('4'_2
'D1,'! 'DE4'1C) AJ 'D*5HJ* D*/J/ E3*B(D 41H7 BHB 'DF41 AJ E4'1J9
HJCJEJ/J' (JF*GJ 'D*5HJ* AJ 3 E'JH 2009). 5H* 'D"F!
7D('* 'D5HD 9DI 'DEF 'D/1'3J) DHJCJE'FJ' 2009 EA*H) 'D"F 3,D 'D"F
[#:DB]
[3'9/F' AJ 'D*1,E)!]
F/9HC DDE3'GE) AJ #3(H9 'D*'1J. 'D93C1J HGH #/ 'D#3'(J9 'DE*9//) EF
#3'(J9 'DHJCJ.
[#:DB]
FB'4 'DE3*./E:9DJ 'D('4' 2
EF HJCJ(J/J' 'DEH3H9) 'D1)
*H,/ D/JC 13'&D ,/J/) (".1 *:JJ1).
Date: 1 Apr 2004 10:30:59 0800
Making use of a new type of modeltheoretic tool the Boolean Sieve
we have been able to construct a Ptime algorithm for SAT, thus
providing a resolution to one of the most famous, longstanding open
problems of Theoretical Computer Science. A detailed, but accessible
and informal, general overview of the Boolean Sieve method (more
information can be found here by carrying out a Google groups search
under "Boolean Sieve" and "Mathematician's Algorithm"). However, a
brief description will be provided below of the method, some
applications outside the specific context of SAT, as well as an
overview of how it was applied to SAT. Opportunity providing, an
abstract or possibly even an online copy of the submitted paper (just
accepted for publication) will be made available at the above Web
site.
What is a Boolean Sieve? Basically, it is a construct that is
generated from a set of models, for an axiomfree theory ("free
theory"), that are defined to filter out the possible logical
relations between a set of statements which could be rendered in that
theory. A possible application may be to seek out significant
axiomatizations that may be applied to the set of operations and
predicates in the underlying free theory. The term "filter" is more
than appropriate given the nature of the formal machinery behind the
method.
For instance, consider Group Theory. An interesting (but not well
known) fact is that groups can be defined by their inverse operation
I Just Proved [P=NP] and I get to announce it on Usenet.
I Just Proved [P=NP] and I get to announce it on Usenet.1
(division), just as well by multiplication. The underlying free theory
is an algebraic sort with the following set of operations:
() |> 1 (identity)
(a, b) |> a/b (quotient)
So, it then becomes natural to ask: what are the logical relations
between the possible statements that could be made over the underlying
free theory. Such a situation is precisely the kind of circumstance
where one would use the Boolean Sieve method.
What one does is write down a bunch of statements (ideally, including
a set of statements that we already know from prior considerations
would completely characterize a group), and then select a bunch of
models for the free theory (which in the case at hand may or may not
actually be groups). Each model should have the property that each
statement has a truth value whose evaluation in that model can be done
"efficiently".
The result is a set of raw data from which a profile can be assembled.
The method of integrating all the basic facts is the Boolean Sieve,
itself. The result of applying the Sieve is an efficient
characterization, as a set of Horn clauses, of the Boolean lattice
generated by the statements. >From there (for instance) one could read
off the significant relations and possible axiomatizations, e.g.,
(a/c)/(b/c) = a/b; a/a = 1; a/1 = a
or for Abelien groups:
a(bc) = c(ba); a(ab) = b; 11 = 1.
More generally, a Boolean Sieve will allow us to filter out the
possible relations between a set of statements. The Sieve is called
Complete for that set, if all possible relations are constructed by
the Sieve. What we've actually done is resolve a generalization of SAT
(i.e., determine the validity of a Horn clause involving Boolean
formulas over Nvariables) by defining a process (that is N^3 in
complexity) that generates a complete Boolean Sieve that is N^3 in
size.
Why N^3? Well, this is where it gets interesting: the method for
generating the complete Boolean Sieve is essentially a disguised
version of the Earley parsing algorithm for contextfree grammars! The
significance and nature of this link remains a total mystery to us.
Currently, we are investigating extensions of the Boolean Sieve which
will provide a basis for modeltheoretic theorem proving methods or
"Semantic Theorem Proving". As any expert mathematician will be able
to relate, such an appropach has a far more direct bearing on the way
mathematicians actually approach problems. They will take a stock set
of examples, run a set of possible statements through the examples
(oftentimes subconsciously) and "magically" arrive at a set of
conjectures. We conjecture that the latent method behind this process
is none other than the Boolean Sieve, itself. We even speculate that
"mathematical intuition", itself, may be nothing more than the by
product of this subconscious process. Thus, for instance, one could
develop a more honed "intuition" by having a larger stock of ready
made examples "under the belt", so to say.
Needless to say, these developments will go far beyond the specifics
of the P = NP problem, as most anyone would have been able to
I Just Proved [P=NP] and I get to announce it on Usenet.
I Just Proved [P=NP] and I get to announce it on Usenet.2
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