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devel / comp.theory / smoke and mirrors: pspace into qspace in linear time and space

SubjectAuthor
* smoke and mirrors: pspace into qspace in linear time and spaceDaniel Pehoushek
`* smoke and mirrors: pspace into qspace in linear time and spaceDaniel Pehoushek
 `* smoke and mirrors: pspace into qspace in linear time and spaceDaniel Pehoushek
  `- smoke and mirrors: pspace into qspace in linear time and spaceDaniel Pehoushek

1
smoke and mirrors: pspace into qspace in linear time and space

<68567db2-1d61-4fb7-82f4-da47c407ad19n@googlegroups.com>

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Subject: smoke and mirrors: pspace into qspace in linear time and space
From: pehoush...@gmail.com (Daniel Pehoushek)
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 by: Daniel Pehoushek - Sun, 17 Jul 2022 11:29 UTC

transform pspace to qspace in fifteen lines of code
in the beginning
s is a set of n bit numbers
that satisfy a boolean n bits equation p

in the beginning then
then smoke and mirrors transforms s of p
into n bit quantifications
that all satisfy s of p
q of p is q
q of q is q

daniel 2380++

// the planning equations
static joy smoke (num v, numnums& s) { when(s.size()==zero || v == qvars.size() ) return;
numnums l; numnums r;split(v,s,l,r); smoke (v+one,l); smoke (v+one,r); mirrors (v,l,r);
for (num g = zero; g < l.size(); g++) { ezis(*(l[g]),v); s.add(l[g]);} l.setsize(zero);
for (num g = zero; g < r.size(); g++) { /*univ(*(r[g]),v);*/ s.add(r[g]);} r.setsize(zero);}

static joy mirrors (num v, numnums& l, numnums& r)
{if(l.size()==zero){for(num g=zero;g<r.size();g++)l.add(r[g]);r.setsize(zero);return;}
when(v == qvars.size()) return;
numnums al; numnums ar; split(v+one, l, al, ar);
numnums bl; numnums br; split(v+one, r, bl, br);
mirrors(v+one, al, bl);mirrors(v+one, ar, br);
for (num g=zero; g < al.size(); g++) l.add(al[g]); for (num g=zero; g < ar.size(); g++) l.add(ar[g]);
for (num g=zero; g < bl.size(); g++) r.add(bl[g]); for (num g=zero; g < br.size(); g++) r.add(br[g]); }

static joy zerotoone(nums& s, num b) { (s[b >> five] += (ones[b & fifthtau])); }
static num be(nums& s, num b) { return (s[b >> five] & (ones[b & fifthtau])); }
static joy ezis(nums& s, num b) { s[b >> five] &= zeroes[b & fifthtau]; }
static joy univ(nums& s, num b) { /*be(s,b);*/ } //
static joy split(num b,numnums&s,numnums&l,numnums& r)
{for(num g=zero;g<s.size();g++)if(be((*s[g]),b))r.add(s[g]);else l.add(s[g]);s.setsize(zero);}

Re: smoke and mirrors: pspace into qspace in linear time and space

<b160f3ed-ab93-4f68-876b-ce65f70c3d5bn@googlegroups.com>

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https://www.novabbs.com/devel/article-flat.php?id=35755&group=comp.theory#35755

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Newsgroups: comp.theory
Date: Sun, 17 Jul 2022 05:25:55 -0700 (PDT)
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Subject: Re: smoke and mirrors: pspace into qspace in linear time and space
From: pehoush...@gmail.com (Daniel Pehoushek)
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 by: Daniel Pehoushek - Sun, 17 Jul 2022 12:25 UTC

On Sunday, July 17, 2022 at 7:29:16 AM UTC-4, Daniel Pehoushek wrote:
> transform pspace to qspace in fifteen lines of code
> in the beginning
> s is a set of n bit numbers
> that satisfy a boolean n bits equation p
>
> in the beginning then
> then smoke and mirrors transforms s of p
> into n bit quantifications
> that all satisfy s of p
> q of p is q
> q of q is q
>
> daniel 2380++
>
> // the planning equations
> static joy smoke (num v, numnums& s) { when(s.size()==zero || v == qvars.size() ) return;
> numnums l; numnums r;split(v,s,l,r); smoke (v+one,l); smoke (v+one,r); mirrors (v,l,r);
> for (num g = zero; g < l.size(); g++) { ezis(*(l[g]),v); s.add(l[g]);} l.setsize(zero);
> for (num g = zero; g < r.size(); g++) { /*univ(*(r[g]),v);*/ s.add(r[g]);} r.setsize(zero);}
>
> static joy mirrors (num v, numnums& l, numnums& r)
> {if(l.size()==zero){for(num g=zero;g<r.size();g++)l.add(r[g]);r.setsize(zero);return;}
> when(v == qvars.size()) return;
> numnums al; numnums ar; split(v+one, l, al, ar);
> numnums bl; numnums br; split(v+one, r, bl, br);
> mirrors(v+one, al, bl);mirrors(v+one, ar, br);
> for (num g=zero; g < al.size(); g++) l.add(al[g]); for (num g=zero; g < ar.size(); g++) l.add(ar[g]);
> for (num g=zero; g < bl.size(); g++) r.add(bl[g]); for (num g=zero; g < br.size(); g++) r.add(br[g]); }
>
> static joy zerotoone(nums& s, num b) { (s[b >> five] += (ones[b & fifthtau])); }
> static num be(nums& s, num b) { return (s[b >> five] & (ones[b & fifthtau])); }
> static joy ezis(nums& s, num b) { s[b >> five] &= zeroes[b & fifthtau]; }
> static joy univ(nums& s, num b) { /*be(s,b);*/ } //
> static joy split(num b,numnums&s,numnums&l,numnums& r)
> {for(num g=zero;g<s.size();g++)if(be((*s[g]),b))r.add(s[g]);else l.add(s[g]);s.setsize(zero);}
s begins as a vector of all satisfying assignments encoded by n bit numbers
the n bit numbers satisfying a boolean n bits equation p
an n bit number is represented by some 32 bit numbers

the quantifications are from union andor intersection
s is transformed into q bit by bit in tree wise fashion
daniel 2380++

Re: smoke and mirrors: pspace into qspace in linear time and space

<e54c2451-6952-4ef8-bec4-ba8c6ca127a6n@googlegroups.com>

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https://www.novabbs.com/devel/article-flat.php?id=35756&group=comp.theory#35756

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Subject: Re: smoke and mirrors: pspace into qspace in linear time and space
From: pehoush...@gmail.com (Daniel Pehoushek)
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 by: Daniel Pehoushek - Sun, 17 Jul 2022 12:31 UTC

On Sunday, July 17, 2022 at 8:25:57 AM UTC-4, Daniel Pehoushek wrote:
> On Sunday, July 17, 2022 at 7:29:16 AM UTC-4, Daniel Pehoushek wrote:
> > transform pspace to qspace in fifteen lines of code
> > in the beginning
> > s is a set of n bit numbers
> > that satisfy a boolean n bits equation p
> >
> > in the beginning then
> > then smoke and mirrors transforms s of p
> > into n bit quantifications
> > that all satisfy s of p
> > q of p is q
> > q of q is q
> >
> > daniel 2380++
> >
> > // the planning equations
> > static joy smoke (num v, numnums& s) { when(s.size()==zero || v == qvars.size() ) return;
> > numnums l; numnums r;split(v,s,l,r); smoke (v+one,l); smoke (v+one,r); mirrors (v,l,r);
> > for (num g = zero; g < l.size(); g++) { ezis(*(l[g]),v); s.add(l[g]);} l.setsize(zero);
> > for (num g = zero; g < r.size(); g++) { /*univ(*(r[g]),v);*/ s.add(r[g]);} r.setsize(zero);}
> >
> > static joy mirrors (num v, numnums& l, numnums& r)
> > {if(l.size()==zero){for(num g=zero;g<r.size();g++)l.add(r[g]);r.setsize(zero);return;}
> > when(v == qvars.size()) return;
> > numnums al; numnums ar; split(v+one, l, al, ar);
> > numnums bl; numnums br; split(v+one, r, bl, br);
> > mirrors(v+one, al, bl);mirrors(v+one, ar, br);
> > for (num g=zero; g < al.size(); g++) l.add(al[g]); for (num g=zero; g < ar.size(); g++) l.add(ar[g]);
> > for (num g=zero; g < bl.size(); g++) r.add(bl[g]); for (num g=zero; g < br.size(); g++) r.add(br[g]); }
> >
> > static joy zerotoone(nums& s, num b) { (s[b >> five] += (ones[b & fifthtau])); }
> > static num be(nums& s, num b) { return (s[b >> five] & (ones[b & fifthtau])); }
> > static joy ezis(nums& s, num b) { s[b >> five] &= zeroes[b & fifthtau]; }
> > static joy univ(nums& s, num b) { /*be(s,b);*/ } //
> > static joy split(num b,numnums&s,numnums&l,numnums& r)
> > {for(num g=zero;g<s.size();g++)if(be((*s[g]),b))r.add(s[g]);else l.add(s[g]);s.setsize(zero);}
> s begins as a vector of all satisfying assignments encoded by n bit numbers
> the n bit numbers satisfying a boolean n bits equation p
> an n bit number is represented by some 32 bit numbers
>
> the quantifications are from union andor intersection
> s is transformed into q bit by bit in tree wise fashion
> daniel 2380++
Informational Pspace of satisfying assignments
transformed into
truthful questions Qspace quantifications

in linear time and in place space

Re: smoke and mirrors: pspace into qspace in linear time and space

<b0cf3445-bf1a-475e-89d4-38c9ce12f783n@googlegroups.com>

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https://www.novabbs.com/devel/article-flat.php?id=35839&group=comp.theory#35839

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Subject: Re: smoke and mirrors: pspace into qspace in linear time and space
From: pehoush...@gmail.com (Daniel Pehoushek)
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 by: Daniel Pehoushek - Mon, 18 Jul 2022 17:19 UTC

On Sunday, July 17, 2022 at 8:31:44 AM UTC-4, Daniel Pehoushek wrote:
> On Sunday, July 17, 2022 at 8:25:57 AM UTC-4, Daniel Pehoushek wrote:
> > On Sunday, July 17, 2022 at 7:29:16 AM UTC-4, Daniel Pehoushek wrote:
> > > transform pspace to qspace in fifteen lines of code
> > > in the beginning
> > > s is a set of n bit numbers
> > > that satisfy a boolean n bits equation p
> > >
> > > in the beginning then
> > > then smoke and mirrors transforms s of p
> > > into n bit quantifications
> > > that all satisfy s of p
> > > q of p is q
> > > q of q is q
> > >
> > > daniel 2380++
> > >
> > > // the planning equations
> > > static joy smoke (num v, numnums& s) { when(s.size()==zero || v == qvars.size() ) return;
> > > numnums l; numnums r;split(v,s,l,r); smoke (v+one,l); smoke (v+one,r); mirrors (v,l,r);
> > > for (num g = zero; g < l.size(); g++) { ezis(*(l[g]),v); s.add(l[g]);} l.setsize(zero);
> > > for (num g = zero; g < r.size(); g++) { /*univ(*(r[g]),v);*/ s.add(r[g]);} r.setsize(zero);}
> > >
> > > static joy mirrors (num v, numnums& l, numnums& r)
> > > {if(l.size()==zero){for(num g=zero;g<r.size();g++)l.add(r[g]);r.setsize(zero);return;}
> > > when(v == qvars.size()) return;
> > > numnums al; numnums ar; split(v+one, l, al, ar);
> > > numnums bl; numnums br; split(v+one, r, bl, br);
> > > mirrors(v+one, al, bl);mirrors(v+one, ar, br);
> > > for (num g=zero; g < al.size(); g++) l.add(al[g]); for (num g=zero; g < ar.size(); g++) l.add(ar[g]);
> > > for (num g=zero; g < bl.size(); g++) r.add(bl[g]); for (num g=zero; g < br.size(); g++) r.add(br[g]); }
> > >
> > > static joy zerotoone(nums& s, num b) { (s[b >> five] += (ones[b & fifthtau])); }
> > > static num be(nums& s, num b) { return (s[b >> five] & (ones[b & fifthtau])); }
> > > static joy ezis(nums& s, num b) { s[b >> five] &= zeroes[b & fifthtau]; }
> > > static joy univ(nums& s, num b) { /*be(s,b);*/ } //
> > > static joy split(num b,numnums&s,numnums&l,numnums& r)
> > > {for(num g=zero;g<s.size();g++)if(be((*s[g]),b))r.add(s[g]);else l.add(s[g]);s.setsize(zero);}
> > s begins as a vector of all satisfying assignments encoded by n bit numbers
> > the n bit numbers satisfying a boolean n bits equation p
> > an n bit number is represented by some 32 bit numbers
> >
> > the quantifications are from union andor intersection
> > s is transformed into q bit by bit in tree wise fashion
> > daniel 2380++
> Informational Pspace of satisfying assignments
> transformed into
> truthful questions Qspace quantifications
>
> in linear time and in place space
Solving all qbfs in fifteen lines should be worthy of gold instead of receiving the null response.
daniel2380++

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