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VMs: deeper investigation on truncated repeating seqs.

To: vms-list@xxxxxxxxxxx
Subject: VMs: deeper investigation on truncated repeating seqs.
From: Marzio De Biasi <voynich@xxxxxxxxxxxx>
Date: Fri, 10 Sep 2004 13:46:32 +0200
In-reply-to: <JAEKJOMCOCMKCPMKKHGMAEGPCKAA.markefincher@travelinfosystem s.com>
References: <200409091610.31348.G.Landini@bham.ac.uk>
Reply-to: vms-list@xxxxxxxxxxx
Sender: owner-vms-list@xxxxxxxxxxx

Hi,
I investigated the Marke Fincher's idea on an excerpt from
the holy bible (~ 190000 chars) and found many sequences like
the ones found by MF on the VM.

I used a very tight algorithm (I think much tighter
than the one used by MF):

1) be N the length of the "starting" string
2) for each UNIQUE sequence SEQ in the VM of length N
   (if it is not unique we should study it in the N+1 case
    as starting string)
   2.1) replace it with @@@@ in the VM
   2.2) set HOLECOUNTER = 0
   2.3) set M = N - 1
   2.4) set SEQLEFT = LEFT(SEQ,M) (leftmost M chars of SEQ)
   2.5) count occurrences of SEQLEFT in the VM
        and replace them with @@@@
        If no occurrency is found HOLECOUNTER = HOLECOUNTER + 1
   2.4) set SEQRIGHT = RIGHT(SEQ,M) (rightmost M chars of SEQ)
   2.6) count occurrences of SEQRIGHT in the VM
        and replace them with @@@@
        If no occurrency is found HOLECOUNTER = HOLECOUNTER + 1
   2.7) if HOLECOUNTER >= MAXHOLECOUNTER then check another sequence
        (restore the VM without @@@ and go to step 2)
   2.8) set M = M - 1 and goto step 2.4 until M > 0
   2.9) print SEQ and its subsequences found in the VM
        (if we arrive at this point SEQ is "good")

   N.B. HOLECOUNTER is a counter for the subsequences
        that miss. MAXHOLECOUNTER is the max number
        of missing sequences allowed (of course for
        shorter values of N, MAXHOLECOUNTER should be
        smaller)

Algorithm flow on an example string and N = 4;

nelYZmezzoXYZWdel minXdi nWosZtra XY vitaYZ mi XYZ rovaiXYZperZW
- analyzing sequence XYZW
nelYZmezzo@@@@del minXdiX nWosZtra XY vitaYZ mi XYZ rovaiXYZperZW
- search for XYZ and YZW
nelYZmezzo@@@@del minXdiX nWosZtra XY vitaYZ mi @@@ rovai@@@perZW
  found 2 XYZ
  found 0 YZW  -> HOLECOUNT = 1
- search for XY and ZW
nelYZmezzo@@@@del minXdiX nWosZtra @@ vitaYZ mi @@@ rovai@@@per@@
  found 1 XY
  found 1 ZW
- searcg for X and W
nelYZmezzo@@@@del min@di@ n@osZtra @@ vitaYZ mi @@@ rovai@@@per@@
  found 2 X
  found 1 W

Output:

X     2
XY    1
XYZ   2
XYZW
  ZW  1
   W  1


For starting len N= 8..12 "tons" of such sequences can be
found.  For greater values of N these sequences are (naturally)
rarer (Marchov chains).


Marke, please post a descritpion of the algorithm
you used in your investigation on "truncated repeating seqs".

Marzio De Biasi

P.S.

These are the results for sequences of length 16 (MAXHOLECOUNTER=8).

. (31465)
.Manasseh.sounds (01074)
.MEans.scarlet.o (00134)
.ME.isaac.means. (00273)
.ME.Have.their.y (00002)
.ME.HEre.he.said (00005)
.ME.HE.left.his. (00004)
.ME.HE.Searched. (00001)
.ME.HE.SAID.god. (00003)
.ME.HE.SAID.TO.m (00001)
.ME.HE.SAID.TO.H
ivE.HE.SAID.TO.H (00001)
ack.HE.SAID.TO.H (00008)
em.sHE.SAID.TO.H (00003)
try.wE.SAID.TO.H (00002)
joseph.SAID.TO.H (00065)
is.handmAID.TO.H (00001)
hich.we.dID.TO.H (00002)
as.gathereD.TO.H (00033)
.they.spoke.TO.H (00101)
e.entered.inTO.H (00007)
.the.angel.whO.H (00039)
ounds.like.the.H (02838)
.the.place.of.tH (09180)

M.sounds.like.th (03018)
MEans.scarlet.or (00354)
ME.isaac.means.h (00676)
ME.Home.they.bro (00006)
ME.HEre.he.said. (00006)
ME.HE.left.his.g (00005)
ME.HE.Searched.b (00001)
ME.HE.SAID.god.b (00005)
ME.HE.SAID.TO.me (00001)
ME.HE.SAID.TO.HI
vE.HE.SAID.TO.HI (00001)
ck.HE.SAID.TO.HI (00008)
n.sHE.SAID.TO.HI (00001)
ry.wE.SAID.TO.HI (00001)
oseph.SAID.TO.HI (00055)
s.handmAID.TO.HI (00001)
ich.we.dID.TO.HI (00002)
s.gathereD.TO.HI (00025)
they.spoke.TO.HI (00081)
.entered.inTO.HI (00007)
e.house.to.dO.HI (00001)
they.embalmed.HI (00905)
y.he.add.terapHI (00656)
the.dead.sheol.I (07028)

. (33197)
.Were.household. (01618)
.WIll.surely.vis (00600)
.WITness.heap.in (00008)
.WITHout.number. (00018)
.WITH.inheritanc (00226)
.WITH.Her.about. (00014)
.WITH.HIs.face.t (00018)
.WITH.HIM.both.c (00043)
.WITH.HIM.To.bur (00001)
.WITH.HIM.THat.w (00002)
.WITH.HIM.THEn.j (00003)
.WITH.HIM.THE.re (00001)
.WITH.HIM.THE.SO
re.to.HIM.THE.SO (00002)
an.husHIM.THE.SO (00001)
d.leummIM.THE.SO (00001)
d.shecheM.THE.SO (00003)
of.machir.THE.SO (00094)
rother.and.HE.SO (00002)
nes.from.herE.SO (00025)
orget.ephraim.SO (00331)
y.have.been.asSO (00111)
l.is.the.place.O (10343)

Of.the.dead. (10424)
OTes.after.god.t (00176)
OTHs.el.elohe.is (00048)
OTHEs.and.every. (00005)
OTHERs.i.am.dyin (00070)
OTHER.will.be.gr (00123)
OTHER.Saying.wha (00010)
OTHER.S.wife.tha (00017)
OTHER.S.Speech.s (00001)
OTHER.S.SONs.bow (00001)
OTHER.S.SON.who. (00001)
OTHER.S.SON.All. (00001)
OTHER.S.SON.AND.
.esau.S.SON.AND. (00002)
hem.hiS.SON.AND. (00002)
.bore.a.SON.AND. (00012)
ken.veniSON.AND. (00003)
ouch.simeON.AND. (00013)
d.of.canaaN.AND. (00098)
e.who.lives.AND. (01623)
f.my.right.hAND. (00289)
which.is.beyoND. (00157)
ace.of.the.deaD. (02810)
he.place.of.the. (29713)

A few results from N = 12 MAXHOLECOUNT=4

Ad. (10160)
ANasseh.soun (00938)
ANDed.before (00094)
AND.sheol.is (01910)
AND.All.that (00089)
AND.ANah.thi (00002)
AND.AND.laid (00023)
AND.AND.Had. (00003)
AND.AND.HE.W
uND.AND.HE.W (00001)
elD.AND.HE.W (00002)
him.AND.HE.W (00010)
he.lAND.HE.W (00002)
s.fouND.HE.W (00001)
.beholD.HE.W (00007)
evening.HE.W (00051)
and.of.tHE.W (00158)
of.the.onE.W (00297)
leed.means.W (01906)
ebrew.for.tW (01056)

Dead. (02089)
D. (04917)
D.Fell.down. (00101)
D.FOur.parts (00010)
D.FORty.seve (00011)
D.FOR.am.i.i (00050)
D.FOR.He.did (00002)
D.FOR.HIm.fo (00001)
D.FOR.HIS.fa (00003)
D.FOR.HIS.Wo (00001)
D.FOR.HIS.WI
h.FOR.HIS.WI (00001)
an.OR.HIS.WI (00001)
bekah.HIS.WI (00038)
oats.tHIS.WI (00001)
rother.IS.WI (00015)
eed.meanS.WI (00102)
ssociated.WI (00777)
brew.for.tWI (00009)
dead.sheol.I (07842)

W.for.twice. (02547)
WIce.fruitfu (00610)
WITness.heap (00008)
WITHout.numb (00017)
WITH.inherit (00271)
WITH.Tambour (00001)
WITH.THat.sa (00002)
WITH.THEir.f (00014)
WITH.THE.fie (00015)
WITH.THE.Exa (00003)
WITH.THE.EAs (00003)
WITH.THE.EAR
onTH.THE.EAR (00002)
nisH.THE.EAR (00001)
k.in.THE.EAR (00103)
ham.rosE.EAR (00006)
y.lord.s.EAR (00013)
red.ten.yEAR (00268)
h.means.scAR (00679)
for.twice.fR (06783)

Is.the.place (07889)
ITful.sheol. (00617)
ITHer.way.or (00032)
ITH.inherita (00271)
ITH.Tambouri (00001)
ITH.THat.sam (00002)
ITH.THEir.fl (00014)
ITH.THE.fiel (00016)
ITH.THE.Exac (00003)
ITH.THE.EAst (00003)
ITH.THE.EART
nTH.THE.EART (00002)
isH.THE.EART (00001)
.of.THE.EART (00102)
e.wholE.EART (00004)
ed.with.EART (00005)
pt.his.hEART (00013)
l.not.depART (00016)
hold.propeRT (00142)
e.place.of.T (10509)

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Follow-Ups:
- VMs: RE: deeper investigation on truncated repeating seqs.
  - From: Marke Fincher
- Re: VMs: deeper investigation on truncated repeating seqs.
  - From: Marzio De Biasi

References:
- Re: VMs: truncated repeating sequences
  - From: Gabriel Landini

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