OKlibrary  0.2.1.6
DopedMUOne.hpp File Reference

Investigations regarding hardness of doped elements of MU(1) More...

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## Detailed Description

Investigations regarding hardness of doped elements of MU(1)

Todo:
Hardness of prime-extremal satisfiable general Horn clause-sets
• The following needs a complete update, based on the arXiv report http://arxiv.org/abs/1302.4421 .
• The clause-sets sat_genhorn_cs(k,l) are candidates to separate representations without new variables of softness l+1 from softness l:
1. sat_genhorn_cs(k,l) itself has hardness min(k,l).
2. So for l >= 0 the sequence S = (sat_genhorn_cs(k,l+1))_{k >= l+1} has a linear-size representation without new variables of hardness precisely l+1, namely itself.
3. Now the conjecture is that S has no polysize representations without new variables of softness l.
4. This is true for l=0, as it follows from the results of the article [Sloan, Soereny, Turan, On k-term DNF with the largest number of prime implicants, 2007].
5. One experiment:
```F : sat_genhorn_cs(3,3)\$
8
P : min_resolution_closure_cs(F)[1]\$
length(P);
255
set_random(1);
B : rand_rbase_cs(P,ucp_0_cs)\$
length(B);
42
set_random(2);
B : rand_rbase_cs(P,ucp_0_cs)\$
length(B);
39
set_random(3);
B : rand_rbase_cs(P,ucp_0_cs)\$
length(B);
38
```
We see here a rather small 1-base.
• A systematic study of the boolean functions of sat_genhorn_cs(k,l) is needed:
1. A good representation (in the general sense) of the underlying boolean function is needed. Perhaps this should go to investigations on boolean functions in general.
2. What is the precise number of variables, clauses, literal occurrences ?
3. What are precisely the prime implicates and prime implicants?
• From Lemma 8 of [Sloan, Soereny, Turan, On k-term DNF with the largest number of prime implicants, 2007] we have the following characterisation of the prime implicates:
```# Extracting the prime implicant from a subset F of the leaves of
# sat_genhorn_cs(k,l):
sat_genhorn_ul(F) := block([lit_s : olit_cs(F)],
subset(lit_s, lambda([l],not(elementp(-l,lit_s)))))\$

# Computing the prime implicates for sat_genhorn_cs(k,l):
sat_genhorn_prime_cs(k,l) :=
map(sat_genhorn_ul, disjoin({},powerset(sat_genhorn_cs(k,l))))\$

# Checking correctness:
F : sat_genhorn_cs(2,2)\$
is(min_resolution_closure_cs(F)[1] = sat_genhorn_prime_cs(2,2));
true
F : sat_genhorn_cs(3,3)\$
is(min_resolution_closure_cs(F)[1] = sat_genhorn_prime_cs(3,3));
true
```
That is, the prime implicates of sat_genhorn_cs(k,l) are precisely the clauses {l in F: -l not in F} for subsets F of sat_genhorn_cs(k,l).
4. What are the m-bases for 0 <= m <= l ?
• Are the sat_genhorn_cs(k,l) actually level-l Horn clause-sets?
Todo:
3 different representations of HIT(1)
• According to [Gywnne, Kullmann, 2013].
• Experiment preparation:
```k:2;
for h in [22,32,42,52,62,72] do (output_ext1_sat_genhorn(h,k),output_ext2_sat_genhorn(h,k),output_ext3_sat_genhorn(h,k));
k:3;
for h in [23,33,43] do (output_ext1_sat_genhorn(h,k),output_ext2_sat_genhorn(h,k),output_ext3_sat_genhorn(h,k));
k:4;
for h in [24,34,44] do (output_ext1_sat_genhorn(h,k),output_ext2_sat_genhorn(h,k),output_ext3_sat_genhorn(h,k));
k:5;
for h in [25,35] do (output_ext1_sat_genhorn(h,k),output_ext2_sat_genhorn(h,k),output_ext3_sat_genhorn(h,k));

> for F in *.ecnf; do B=\$(basename --suffix=".ecnf" \${F}); echo \${B}; cat \${F} | ExtendedToStrictDimacs-O3-DNDEBUG > \${B}.cnf; done
```
• Determining the sizes:
```for F in *.cnf; do echo \${F} " "; cat \${F} | ExtendedDimacsStatistics-O3-DNDEBUG; done
E1_SAT_genhorn_22_2.cnf
n       c   l
507     508   8604
E1_SAT_genhorn_23_3.cnf
n       c   l
4095    4096   80594
E1_SAT_genhorn_24_4.cnf
n       c   l
25901   25902   562542
E1_SAT_genhorn_25_5.cnf
n       c   l
136811  136812   3202912
E1_SAT_genhorn_32_2.cnf
n       c   l
1057    1058   24994
E1_SAT_genhorn_33_3.cnf
n       c   l
12035   12036   327384
E1_SAT_genhorn_34_4.cnf
n       c   l
105911  105912   3150408
E1_SAT_genhorn_35_5.cnf
n       c   l
768335  768336   24413776
E1_SAT_genhorn_42_2.cnf
n       c   l
1807    1808   54784
E1_SAT_genhorn_43_3.cnf
n       c   l
26575   26576   922524
E1_SAT_genhorn_44_4.cnf
n       c   l
299971  299972   11326724
E1_SAT_genhorn_52_2.cnf
n       c   l
2757    2758   101974
E1_SAT_genhorn_62_2.cnf
n       c   l
3907    3908   170564
E1_SAT_genhorn_72_2.cnf
n       c   l
5257    5258   264554
E2_SAT_genhorn_22_2.cnf
n       c   l
761    4811   17716
E2_SAT_genhorn_23_3.cnf
n       c   l
6143   44394   165284
E2_SAT_genhorn_24_4.cnf
n       c   l
38852  307174   1150986
E2_SAT_genhorn_25_5.cnf
n       c   l
205217 1738269   6542636
E2_SAT_genhorn_32_2.cnf
n       c   l
1586   13556   51046
E2_SAT_genhorn_33_3.cnf
n       c   l
18053  175729   666804
E2_SAT_genhorn_34_4.cnf
n       c   l
158867 1681117   6406728
E2_SAT_genhorn_35_5.cnf
n        c   l
1152503 12975225  49595888
E2_SAT_genhorn_42_2.cnf
n       c   l
2711   29201   111376
E2_SAT_genhorn_43_3.cnf
n       c   l
39863  487839   1871624
E2_SAT_genhorn_44_4.cnf
n       c   l
449957 5963335   22953420
E2_SAT_genhorn_52_2.cnf
n       c   l
4136   53746   206706
E2_SAT_genhorn_62_2.cnf
n       c   l
5861   89191   345036
E2_SAT_genhorn_72_2.cnf
n       c   l
7886  137536   534366
E3_SAT_genhorn_22_2.cnf
n       c   l
761    4557   13160
E3_SAT_genhorn_23_3.cnf
n       c   l
6143   42346   122939
E3_SAT_genhorn_24_4.cnf
n       c   l
38852  294223   856764
E3_SAT_genhorn_25_5.cnf
n       c   l
205217 1669863   4872774
E3_SAT_genhorn_32_2.cnf
n       c   l
1586   13027   38020
E3_SAT_genhorn_33_3.cnf
n       c   l
18053  169711   497094
E3_SAT_genhorn_34_4.cnf
n       c   l
158867 1628161   4778568
E3_SAT_genhorn_35_5.cnf
n       c   l
1152503 12591057  37004832
E3_SAT_genhorn_42_2.cnf
n       c   l
2711   28297   83080
E3_SAT_genhorn_43_3.cnf
n       c   l
39863  474551   1397074
E3_SAT_genhorn_44_4.cnf
n       c   l
449957 5813349   17140072
E3_SAT_genhorn_52_2.cnf
n       c   l
4136   52367   154340
E3_SAT_genhorn_62_2.cnf
n       c   l
5861   87237   257800
E3_SAT_genhorn_72_2.cnf
n       c   l
7886  134907   399460
```
• Compiling satz:
```ExternalSources> CPPFLAGS="-DMAX_CLAUSE_LENGTH=1000000 -DMAX_NUMBER_VARIABLES=2000000 -DMAX_NUMBER_CLAUSES=15000000" oklib satz
```
• Running experiments (on cs-wsok; file "Problems" contains all problems, "Problems23" those of type 2,3):
```> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; OKsolver_2002-O3-DNDEBUG --timeout=7200 \${F} > \${B}.oksolver; done
(E2_SAT_genhorn_35_5: aborted after 27097.7s and ~ 26 GB)

> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; OKsolver_2002_NTP-O3-DNDEBUG \${F} > \${B}.oksolver-ntp; done

> for F in \$(cat Problems23); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; satz215 \${F} > \${B}.satz; done

> for F in \$(cat Problems); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; glucose-2.0 \${F} > \${B}.glucose; done
(E2_SAT_genhorn_44_4: aborted after 535 min)
(E3_SAT_genhorn_44_4: aborted after 518 min)
(E2_SAT_genhorn_35_5: aborted after 674 min)
(E3_SAT_genhorn_35_5: aborted after 538 min)

> for F in \$(cat Problems); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; glucose-2.2 \${F} > \${B}.glucose22; done
(E2_SAT_genhorn_44_4: aborted after 1513m)
(E3_SAT_genhorn_44_4: aborted after 1140m)
(E2_SAT_genhorn_35_5: aborted after 6240m)
(E3_SAT_genhorn_35_5: aborted after 1298m)

> for F in \$(cat Problems); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; glucose-2.2 -no-pre \${F} > \${B}.glucose22-no; done
(E2_SAT_genhorn_44_4: aborted after 1516m)
(E3_SAT_genhorn_44_4: aborted after 1735m)
(E2_SAT_genhorn_35_5: aborted after 1441m)
(E3_SAT_genhorn_35_5: aborted after 1355m)

> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; picosat913 \${F} > \${B}.picosat; done
(E1_SAT_genhorn_35_5: gives up after 478.5 sec)
(E2_SAT_genhorn_35_5: out of memory, > 20 GB)
(E3_SAT_genhorn_35_5: out of memory, > 30 GB)
(E3_SAT_genhorn_44_4: out of memory, > 30 GB)
(E2_SAT_genhorn_44_4: out of memory, > 30 GB)

> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; precosat-570.1 -v \${F} > \${B}.precosat; done

> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; lingelingala-b02aa1a-121013 -v \${F} > \${B}.lingeling; done
(aborted on E2_SAT_genhorn_35_5 after 11464 min, on E2_SAT_genhorn_44_4 after
1571 min, on E3_SAT_genhorn_35_5 after 1580 min, on E3_SAT_genhorn_44_4 after
1015 min)
> ls *.cnf > AllProblems
> cp AllProblems ProblemsLingeling
> for F in \$(cat ProblemsLingeling); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; lingelingala-b02aa1a-121013 -v \${F} > \${B}.lingeling; done

ls *_2.cnf > Problems; ls *_3.cnf >> Problems; ls *_4.cnf >> Problems; ls *_5.cnf >> Problems

> for F in \$(cat Problems); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; minisat-2.2.0 -no-pre \${F} > \${B}.minisat-no; done
(E2_SAT_genhorn_44_4: aborted after 848 min)
(E3_SAT_genhorn_44_4: aborted after 533 min)
(E2_SAT_genhorn_35_5: segmentation fault)
(E3_SAT_genhorn_35_5: got killed by accident, > 600 min)

> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; minisat-2.2.0 \${F} > \${B}.minisat; done
(E2_SAT_genhorn_35_5: aborted after 1511 min)
(E2_SAT_genhorn_44_4: aborted after 296 min)
(E3_SAT_genhorn_35_5: aborted after 1011 min)
(E3_SAT_genhorn_44_4: segmentation fault)

> for F in *.cnf; do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; cryptominisat \${F} > \${B}.cryptominisat_296; done
(for E2_SAT_genhorn_35_5.cnf and E3_SAT_genhorn_35_5.cnf there are too long
clauses to be handled by it)

> for F in \$(cat Problems); do B=\$(basename --suffix=".cnf" \${F}); echo \${B}; march_pl \${F} > \${B}.march; done
(can't solve E2_SAT_genhorn_23_3, E3_SAT_genhorn_23_3 due to
Assertion `btb_size[ i ] == 0' failed)
(can't solve E2_SAT_genhorn_33_3, E3_SAT_genhorn_33_3 due to
segmentation fault)
(E1_SAT_genhorn_34_4: aborted after 370 min)
other instances not tried
```
• Extracting statistics:
```sfile="OKsolver.stats"
ssuffix=".oksolver"
sextract="ExtractOKsolver"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="OKsolver-ntp.stats"
ssuffix=".oksolver-ntp"
sextract="ExtractOKsolver"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Satz.stats"
ssuffix=".satz"
sextract="ExtractSatz"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Glucose.stats"
ssuffix=".glucose"
sextract="ExtractGlucose"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Glucose22.stats"
ssuffix=".glucose22"
sextract="ExtractGlucose"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Glucose22-no.stats"
ssuffix=".glucose22-no"
sextract="ExtractGlucose"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Picosat.stats"
ssuffix=".picosat"
sextract="ExtractPicosat"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Precosat570.stats"
ssuffix=".precosat"
sextract="ExtractPrecosat570"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Lingeling.stats"
ssuffix=".lingeling"
sextract="ExtractLingeling"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Minisat.stats"
ssuffix=".minisat"
sextract="ExtractMinisat"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Minisat-no.stats"
ssuffix=".minisat-no"
sextract="ExtractMinisat"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Cryptominisat296.stats"
ssuffix=".cryptominisat_296"
sextract="ExtractCryptominisat"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done

sfile="Marchpl.stats"
ssuffix=".march"
sextract="ExtractMarchpl"
echo -n "type k h " > \${sfile}
for ((k=2; k <= 5; ++k)); do for F in *_\${k}\${ssuffix}; do T=\$(echo \${F} | cut -d"_" -f1 | cut -d"E" -f2); H=\$(echo \${F} | cut -d"_" -f4); K=\$(basename --suffix="\${ssuffix}" \${F} | cut -d"_" -f5); echo -n "\$T \$K \$H " >> \${sfile}; cat \${F} | \${sextract} extract >> \${sfile}; done; done
```
• Evaluation:
```> E=read_satstat("OKsolver.stats")
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0 0.1 0.1 0.3 0.6
1 3 : 0 0.3 1.5
1 4 : 0.5 4.2 24.3
1 5 : 3.5 52
2 2 : 0 0 0.2 1.7 4.8 11.6
2 3 : 0.3 16.9 135.5
2 4 : 36.2 1164.6
2 5 : 932.1
3 2 : 0 0 0.1 0.4 1.1 5.1
3 3 : 0.1 6.9 65.3
3 4 : 17.9 638.7
3 5 : 553.7
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$nds[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 43 63 83 103 123 143
1 3 : 507 1057 1807
1 4 : 4095 12035 26575
1 5 : 25901 105911
2 2 : 1 1 1 1 1 1
2 3 : 1 1 1
2 4 : 1 1
2 5 : 1
3 2 : 1 1 1 1 1 1
3 3 : 1 1 1
3 4 : 1 1
3 5 : 1

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0 0 0.1 0.2 0.4
1 3 : 0 0.2 1
1 4 : 0.4 3.3 16.5
1 5 : 2.7 31.2
2 2 : 0 0 0.1 0.4 1 4
2 3 : 0.2 4.8 82.6
2 4 : 15.4 843.4 10232.8
2 5 : 664.6 36743.4
3 2 : 0 0 0.1 0.2 0.5 1
3 3 : 0.1 1.6 28.9
3 4 : 4.5 410.8 5295.6
3 5 : 348.7 20061.6
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$nds[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 43 63 83 103 123 143
1 3 : 507 1057 1807
1 4 : 4095 12035 26575
1 5 : 25901 105911
2 2 : 1 1 1 1 1 1
2 3 : 1 1 1
2 4 : 1 1 1
2 5 : 1 1
3 2 : 1 1 1 1 1 1
3 3 : 1 1 1
3 4 : 1 1 1
3 5 : 1 1

> for (t in seq(2,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
2 2 : 0.09 0.68 3.89 13.8 37.66 89.93
2 3 : 7.83 161.78 1326.47
2 4 : 469.46 12956.74 143558
2 5 : 13419.7 609055.6
3 2 : 0.04 0.3 1.6 5.73 16.7 39.47
3 3 : 2.79 66.92 521.59
3 4 : 205.45 5666.27 60673.13
3 5 : 5518.24 250076
> for (t in seq(2,3)) for (k in seq(2,5)) cat(t,k,":",E\$nds[E\$type==t & E\$k==k & E\$sat==0],"\n")
2 2 : 37 57 77 97 117 137
2 3 : 381 871 1561
2 4 : 2701 9051 21401
2 5 : 15093 72913
3 2 : 37 57 77 97 117 137
3 3 : 381 871 1561
3 4 : 2701 9051 21401
3 5 : 15093 72913

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0.11 0.89 4.17 14.77 41.26 100.15
1 3 : 5.33 90.37 763.13
1 4 : 190.6
1 5 :
2 2 : 0.14 1.24 6.98 13.98 38.89 513.06
2 3 : 617.42
2 4 :
2 5 :
3 2 : 0.04 0.34 1.86 25.01 93.8 228.52
3 3 : 940.86
3 4 :
3 5 :
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$nds[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 14 20 25 31 36 42
1 3 : 41 61 81
1 4 : 463
1 5 :
2 2 : 11 13 17 1 1 1
2 3 : 1
2 4 :
2 5 :
3 2 : 19 25 31 1 1 1
3 3 : 1
3 4 :
3 5 :

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0.001999 0.005999 0.018997 0.035994 0.050992 0.19297
1 3 : 0.051992 0.517921 2.54861
1 4 : 2.95555 73.1469 538.97
1 5 : 102.221 4249.87
2 2 : 0.006998 0.026995 0.101984 0.19497 0.476927 1.01185
2 3 : 0.387941 19.0391 98.67
2 4 : 93.4108 5889.3
2 5 : 12921.5
3 2 : 0.004999 0.027995 0.088986 0.188971 0.470928 0.98285
3 3 : 0.429934 13.074 107.865
3 4 : 73.5918 5556.63
3 5 : 11711.3
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 350 853 1371 2017 3003 3969
1 3 : 3642 9976 21567
1 4 : 23265 92344 287335
1 5 : 129523 816139
2 2 : 383 934 1594 2694 3786 6127
2 3 : 2601 8770 22453
2 4 : 16170 73007
2 5 : 83431
3 2 : 400 929 1544 2588 3800 6127
3 3 : 2626 8633 22331
3 4 : 16463 75795
3 5 : 83959

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0.003999 0.021996 0.081987 0.226965 0.540917 1.12483
1 3 : 0.169974 2.18467 14.6958
1 4 : 5.80812 159.142 1910.98
1 5 : 152.08 9959.28
2 2 : 0.008998 0.046992 0.285956 0.45693 1.04484 1.3138
2 3 : 0.095985 16.6885 169.929
2 4 : 11.7832 9479.15
2 5 : 4903.1
3 2 : 0.007998 0.044993 0.266959 0.439933 1.04084 1.2868
3 3 : 0.089986 16.3895 180.317
3 4 : 12.4651 7804.1
3 5 : 3115.65
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0 0 0 0 0
1 3 : 0 0 0
1 4 : 0 0 0
1 5 : 0 0
2 2 : 117 821 1815 2780 4049 5428
2 3 : 1203 8357 21365
2 4 : 10756 79382
2 5 : 74150
3 2 : 117 821 1810 2855 4034 5428
3 3 : 1203 8725 20823
3 4 : 10558 73212
3 5 : 70752

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0.001999 0.004999 0.018997 0.037994 0.087986 0.108983
1 3 : 0.071989 0.526919 1.9977
1 4 : 2.80157 43.8503 537.935
1 5 : 115.842 2728.58
2 2 : 0.004999 0.021996 0.067989 0.180972 0.39194 0.780881
2 3 : 0.514921 7.62484 102.642
2 4 : 75.2306 6502.82
2 5 : 9026.88
3 2 : 0.004999 0.019996 0.067989 0.178972 0.387941 0.778881
3 3 : 0.504923 11.4183 108.266
3 4 : 93.5008 5427.91
3 5 : 9719.65
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 350 828 1337 2098 2869 4134
1 3 : 3175 9642 21837
1 4 : 21260 85660 269273
1 5 : 118088 700202
2 2 : 372 944 1581 3149 4127 5707
2 3 : 2681 8222 21333
2 4 : 16919 79964
2 5 : 83562
3 2 : 372 944 1586 3153 4072 5751
3 3 : 2711 8333 21424
3 4 : 17800 73399
3 5 : 81337

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0 0 0 0.1 0.1
1 3 : 0.1 0.4 1.5
1 4 : 1.3 15.9 135.7
1 5 : 25.6
2 2 : 0 0 0 0.1 0.1 0.2
2 3 : 0.1 3.6 125.1
2 4 : 44.5 5110.2
2 5 : 5523.5
3 2 : 0 0 0 0 0.1 0.1
3 3 : 0.1 3.8 125.2
3 4 : 53.5 5822.1
3 5 : 6540.2
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 254 585 964 1411 2023 2689
1 3 : 2217 6261 13635
1 4 : 13337 54002 152931
1 5 : 69336
2 2 : 254 529 904 1379 1954 2629
2 3 : 2048 7808 20567
2 4 : 16283 73501
2 5 : 83821
3 2 : 254 529 904 1379 1954 2629
3 3 : 2048 7774 20760
3 4 : 16270 73540
3 5 : 83829

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0 0 0.1 0.1 0.2
1 3 : 0 0.2 1.1
1 4 : 0.5 9.2 94.2
1 5 : 10.1 389
2 2 : 0 0.1 0.4 0.9 2 4.1
2 3 : 0.9 8.8 53.9
2 4 : 30.4 751.9 35356
2 5 : 3635.8
3 2 : 0 0.1 0.4 1 2.2 4.4
3 3 : 0.9 8.7 54.7
3 4 : 29.9 735.8 44808.4
3 5 : 3484.4
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 1 1 1 1 1 1
1 3 : 1 1 1
1 4 : 1 1 1
1 5 : 1 1
2 2 : 16 20 560 1438 2398 3493
2 3 : 17 209 17295
2 4 : 857 64688 410510
2 5 : 31092
3 2 : 16 20 560 1438 2398 3493
3 3 : 17 209 17295
3 4 : 857 64688 410510
3 5 : 31092

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0.2 0.3 0.5 2.1 3.8
1 3 : 0.9 7 54.6
1 4 : 33.2 389.4 3139
1 5 : 479.6 14845.9
2 2 : 0 0 0 0.1 1.4 3.4
2 3 : 0.3 15.6 834.3
2 4 : 201 25004.9
2 5 : 37201.4
3 2 : 0 0 0 0.1 1.2 1.6
3 3 : 0.3 34.8 683.6
3 4 : 411 18593.2
3 5 : 19148.9
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 100 100 100 100 1528 2100
1 3 : 655 4470 13585
1 4 : 13324 54187 152934
1 5 : 70177 392047
2 2 : 100 100 100 100 338 835
2 3 : 100 4822 28616
2 4 : 19113 103069
2 5 : 124208
3 2 : 100 100 100 100 343 745
3 3 : 100 4941 29862
3 4 : 20978 119524
3 5 : 117605

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0.003999 0.021996 0.080987 0.234964 0.546916 1.14083
1 3 : 0.158975 2.06669 14.5708
1 4 : 5.48017 149.517 2117.11
1 5 : 143.273 11635.8
2 2 : 0.006998 0.045993 0.152976 0.597909 1.06584 2.6626
2 3 : 0.100984 15.0077 132.493
2 4 : 10.0605 6380.75
2 5 : 3281.57
3 2 : 0.008998 0.044993 0.142978 0.559914 0.991849 2.42663
3 3 : 0.088986 14.8467 134.714
3 4 : 9.93149 6894.03
3 5 : 3208.5
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0 0 0 0 0
1 3 : 0 0 0
1 4 : 0 0 0
1 5 : 0 0
2 2 : 136 740 1529 2778 3887 5417
2 3 : 1276 8333 20033
2 4 : 10427 72123
2 5 : 67344
3 2 : 136 740 1529 2778 3887 5417
3 3 : 1276 8272 19939
3 4 : 10330 70250
3 5 : 66739

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0 0.007998 0.017997 0.032994 0.06499 0.097985
1 3 : 0.077988 0.613906 3.32849
1 4 : 3.39048 62.2055 475.672
1 5 : 74.8946 2633.26
2 2 : 0.005999 0.030995 0.06399 0.164974 0.383941 1.35279
2 3 : 0.529919 10.3664 89.5344
2 4 : 71.8081 5375.87
2 5 : 4044.13
3 2 : 0.003999 0.027995 0.06399 0.153976 0.374943 1.26481
3 3 : 0.516921 10.4744 90.9752
3 4 : 62.2405 4749.34
3 5 : 4057.69
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 365 795 1366 1962 2861 3963
1 3 : 3344 10163 23355
1 4 : 23307 88280 232867
1 5 : 109898 608180
2 2 : 416 905 1563 2496 3697 4981
2 3 : 2719 8213 20101
2 4 : 15761 69651
2 5 : 82751
3 2 : 416 905 1563 2496 3697 4981
3 3 : 2683 8217 19817
3 4 : 15761 69651
3 5 : 82751

> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$t[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 0.01 0.02 0.04 0.11 0.22 0.45
1 3 : 0.09 0.74 4.83
1 4 : 2.5 57.78 538.63
1 5 : 76.51 4440.04
2 2 : 0 0.01 0.02 0.04 0.07 0.11
2 3 : 0.06 0.4 0.97
2 4 : 1.1 706.17 34460.56
2 5 : 1323.26
3 2 : 0 0.01 0.01 0.03 0.06 0.09
3 3 : 0.05 0.35 1.15
3 4 : 1.36 614.75 34849.85
3 5 : 1282.69
> for (t in seq(1,3)) for (k in seq(2,5)) cat(t,k,":",E\$cfs[E\$type==t & E\$k==k & E\$sat==0],"\n")
1 2 : 20 25 53 50 55 56
1 3 : 349 1426 12547
1 4 : 14335 65608 332497
1 5 : 66235 942020
2 2 : 0 0 0 0 0 0
2 3 : 0 0 0
2 4 : 0 30501 114958
2 5 : 30561
3 2 : 0 0 0 0 0 0
3 3 : 0 0 0
3 4 : 0 30500 105312
3 5 : 30500
```
• From the look-ahead solvers OKsolver2002 is far best, and also likely overall the best.
• Some regressions:
```E = read_satstat("OKsolver-ntp.stats")

Et1 = E[E\$type == 1,]
m = lm(Et1\$t ~ Et1\$l)
summary(m)
Min       1Q   Median       3Q      Max
-1.32137 -0.13701  0.08398  0.14693  1.84109
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.726e-01  2.118e-01  -0.815    0.431
Et1\$l        1.309e-06  2.902e-08  45.125 9.14e-15 ***
Residual standard error: 0.713 on 12 degrees of freedom
Multiple R-squared: 0.9941,     Adjusted R-squared: 0.9937
F-statistic:  2036 on 1 and 12 DF,  p-value: 9.145e-15

plot(Et1\$l,Et1\$t)
lines(Et1\$l,predict(m))

Et23 = E[E\$type != 1,]
v = as.double(Et23\$l) * as.double(Et23\$n)
m23 = lm(Et23\$t ~ v)
summary(m23)
Min      1Q  Median      3Q     Max
-5128.9  -105.6  -102.1  -101.9  4055.2
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.019e+02  2.838e+02   0.359    0.723
v           5.883e-10  2.072e-11  28.398   <2e-16 ***
Residual standard error: 1424 on 26 degrees of freedom
Multiple R-squared: 0.9688,     Adjusted R-squared: 0.9676
F-statistic: 806.4 on 1 and 26 DF,  p-value: < 2.2e-16

plot(Et23\$t)
lines(predict(m23))
```

Definition in file DopedMUOne.hpp.