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Best known Regex Golf solutions (SPOILERS) - Classic level set - (SPOILERS)

Collected solutions for Regex Golf, Classic level set

See also:
jpsim gist (discussion)
jonathanmorley gist (discussion)
teukon's Draft Regex Golf Bonus Levels
Solutions to teukon's Draft Regex Golf Bonus Levels (SPOILERS! SPOILERS!) and discussion of mathematical regexes
Continued discussion of Regex Golf Bonus Levels and mathematical regexes (SPOILERS! SPOILERS!)

Please let me know if you find any errors here, or can fill in any of the missing data.

Timestamps are in UTC. Be careful when following GitHub comment links – spoilers may be seen for other levels.

If I manage to discover solutions matching the unpublished high-score holders in length, I'm leaning towards publishing them here only as md5sums, so as not to further taint the high-score lists on Regex Golf.

There are some very wide tables below, which are uncomfortably constrained by the GitHub frameworks CSS. So I would suggest using a browser plugin to override the style with gist-wide.css.

Key to credits:

Exact solutions (to the test cases)

Level Length Regex Date Credit
Plain strings 3 one of the below before 2013-12-20 alok (RG~)
  3 foo 2013-12-20 11:18:54 Rhomboid (R)
  foo 2013-12-20 14:01:04 ZirconCode (HN)
  f.o 2014-01 Peter Norvig
Anchors 2 k$ before 2013-12-20 alok (RG~)
It never ends 6 u(?!.)
  3 u\b
Ranges 8 one of the below before 2013-12-20 alok (RG~)
  8 ^[a-f]*$ 2013-12-20 11:18:54 Rhomboid (R)
  [a-f]{4} 2013-12-20 14:09:44 Sir_Cmpwn (HN)
  [a-g]{4}
  [a-h]{4}
  ^[a-g]*$ 2013-12-20 15:47:57 chingjun (HN)
  ^[a-f]*$ 2013-12-20 18:09:39 josephlord (HN)
  ^[a-h]*$
Backrefs 9 (...).*\1 before 2013-12-20 alok (RG~)
Abba 14 ^(?!(.)+\1)|ef 2013-12-26 14:37:35 sammiya (GH)
  14 one of the above or below 2014-01-07 12:27:38 cesium (RG~) (discovery date is earlier than indicated date)
  14 ^(?!(.)+\1)|.u 2017-07-27 13:21:15 depperm (GH)
  14 ^(?!(.)+\1)|fu
A man, a plan 13 almost certainly one of the below before 2013-12-20 Scott (RG~)
  13 ^(.)[^p].*\1$ 2013-12-20 12:10:04 Bisqwit (R)
  ^(.)[^p].*\1$ 2013-12-20 15:43:30 hyp0 (HN)
  ^(.)[^p].+\1$
  15 ^(\w(?!p)).*\1$ 2013-12-20 18:48:59 Athox (R) - edited 2013-12-20 20:23:59
Prime 14 ^(?!(11+)\1+$)**** 1997-10-22 18:17:07 Abigail (P)
  14 one of the below before 2013-12-20 alok (RG~)
  14 ^(?!(xx+)\1+$) 2013-12-20 11:18:54 Rhomboid (R)
  14 ^(?!(xx+)\1+$) 2013-12-20 12:10:04 Bisqwit (R)
  14 ^(?!(x+x)\1+$)
  14 ^(?!(.+.)\1+$)
  14 ^(?!(..+)\1+$)
  16 ^(?!(..+)(\1)+$) 2013-12-20 16:14:12 josephlord (HN)
Four 11 (.)(.\1){3} before 2013-12-20 alok (RG~)
  14 ([aeio]).{5}\1 2013-12-20 11:18:54 Rhomboid (R)
  11 (.)(.\1){3} 2013-12-20 12:10:04 Bisqwit (R)
  (.)(.\1){3} 2013-12-20 13:13:38 osuushi (R)
  (.)(.\1){3} 2013-12-20 15:05:14 chrismorgan (HN)
Order 11 ^[^o]?.{5}$ before 2013-12-20 andersk (RG~,GH)
  11 ^.{5}[^e]?$ 2013-12-20 12:10:04 Bisqwit (R)
  11 ^.{5}[^e]?$ 2013-12-20 16:13:09 noggin-scratcher (R)
  ^.{5}[^e]?$ 2013-12-20 21:50:12 ekke (HN)
  ^[^o]?.{5}$ 2013-12-20 22:13:14 balrok (GH)
Triples 34 [02-5][123][257]|[07][0269]+3?$|55 before 2013-12-20 andersk (RG~,GH)
  56 ^(([147]4|40|3[269]|9[05]|[378]1).+|0[369]*|[81][257])*$ 2013-12-20 12:10:04 Bisqwit (R)
  44 ^[387][12479]|00($|[369]|1[25])|5[54]|2[437] 2013-12-21 10:05:27 grobie (GH)
  40 00($|[369]|1[25])|(^.|9|3)..5|4.2|^[38]1 2013-12-23 03:15:47 alexandrosm (GH)
  39 32|.[25][345].|00([369]|1[25]|$)|[07]2$ 2013-12-23 07:10:33 rabcyr (GH)
  36 00([369]|1[25]|$)|.1.+4|3.*7.|4.2|55 2013-12-23 12:55:08 alexandrosm (GH)
  34 00($|3|6|9|12|15)|4.2|.1.+4|55|.17 2013-12-23 21:02:53 alexandrosm (GH)
Glob 17 [unpublished] before 2013-12-20 andersk (RG~,GH)
  23 ai|c$|^p|[bcnrw][bnopr] 2013-12-21 18:37:50 nwellnhof (HN)
  [bncrw][bporn]|^p|c$|ta 2013-12-23 16:04:15 bbarry (GH) - some regexes in this comment were edited after the indicated date; may include this regex
  [bcnrw][bnopr]|^p|t[a*] 2018-12-01 Davidebyzero (GH,RG)
  [bcnrw][bnopr]|^p|en.?t 2018-12-01 Davidebyzero (GH,RG)
  [cnprw][opr]|le\w|ai|c$ 2018-12-08 Davidebyzero (GH,RG)
  [cnprw][opr]|le\w|ta|c$ 2018-12-08 Davidebyzero (GH,RG)
  [cnprw][opr]|le\w|t[a*] 2018-12-08 Davidebyzero (GH,RG)
  [cnprw][opr]|le\w|en.?t 2018-12-08 Davidebyzero (GH,RG)
  [^rt][cenprw][n-r][a-t] 2019-12-10 08:46:41 Davidebyzero (GH,RG)
  60 ^(.*)\*(.*) .* \1.+\2$|^(.+) .* \3$|^.*\*(.*)\*.* .* .+\4.+$ 2014-01-08 18:00:49 sorcio (GH)
  66 ^(.*) .* \1$|^(.*)\*(.*) .* \2.+\3$|(.*)\*(.*)\*(.*) .* \4.+\5.+\6 2014-01-13 04:30:24 sshock (GH)
  54 ^((\w*)( .+ \2$|\*(\w*)( .+ \2.+\4$|\*.* .+ \2.+\4.))) 2014-02-13 04:55:56 Davidebyzero (GH)
  50 ^((.*)(.+ \2$|\*(.*)( .+ \2.+\4$|\*.*.+ \2.+\4.))) 2018-12-11 Davidebyzero (GH)
  22 [unpublished] 2016-11…2017-01 ≈ Gael (RG)
  22 [unpublished] 2019-12-06 12:27:55 Davidebyzero (GH, RG)
  21 [unpublished] 2018-02 ≈ LLB (RG)
Balance 24 [unpublished] before 2013-12-20 andersk (RG~,GH)
  34 ^(<(<(<(<(<(<.*>)*>)*>)*>)*>)*>)*$ 2013-12-20 15:24:00 Overv (R) - edited 2013-12-20 15:56:16; it is unknown if the regex was longer before the edit
  ^(<(<(<(<(<(<<>>)*>)*>)*>)*>)*>)*$ 2013-12-20 16:13:39 nadinengland (HN)
  33 ^(<(<(<(<(<(<.*)*>)*>)*>)*>)*>)*$ 2013-12-20 18:39:40 jensweh (R)
  32 ^(<(<(<(<(<>)*>|.{9})*>)*>)*>)*$ 2014-01-02 22:55:11 alexandrosm (GH)
  31 ^(<(<(<(<<?>?>|.{9})*>)*>)*>)*$ 2014-01-05 14:04:09 alexandrosm (GH)
  28 ^$|.{37}|^<(.(?!><*.>$).)*>$ 2014-02-27 01:49:48 Davidebyzero (GH,RG)
  26 .{37}|^(<(..(?!<.>$))*>)*$ 2014-03-23 08:47:49 Davidebyzero (GH,RG)
  22 [unpublished] 2018-10-23…2018-12≈ TH (RG)
Powers 17 one of the 17-scoring ones below before 2013-12-20 andersk (RG~,GH)
  54 ^((((((((((x)\10?)\9?)\8?)\7?)\6?)\5?)\4?)\3?)\2?)\1?$ 2013-12-20 13:26:43 Iwonderifthisistaken (R)
  52 ^xx?$|^((((((((x{4})\8?)\7?)\6?)\5?)\4?)\3?)\2?)\1?$ 2013-12-20 15:07:07 Hrafnahnef (R)
  52 ^((xx?)\2?|(((((((x{8})\9?)\8?)\7?)\6?)\5?)\4?)\3?)$ 2013-12-20 15:18:10 Bisqwit (R)
  51 ^(x|(xx){1,4}|((((((x{16})\8?)\7?)\6?)\5?)\4?)\3?)$ 2013-12-20 15:26:55 Bisqwit (R)
  41 ^(x|(xx){1,10}|(x{32}){1,4}|(x{32}){6,})$ 2013-12-20 18:16:49 Iwonderifthisistaken (R)
  50 ^(((((((((xx?)\9?)\8?)\7?)\6?)\5?)\4?)\3?)\2?)\1?$ 2013-12-20 18:39:40 jensweh (R)
  30 ^(((x|x{8}|x{128})\3?)\2?)\1?$ 2013-12-20 18:43:08 pondscum (R)
  17 ^(?!(.(..)+)\1*$) 2013-12-20 19:18:06 plby (GH)
  ^(?!(x(xx)+)\1*$)
  ^(?!((xx)+x)\1*$)
  ^(?!((..)+.)\1*$)
  36 ^(x{64})+$|^((((x?x)\5?)\4?)\3?)\2?$ 2013-12-20 23:36:55 q1u2acker (R)
  33 ^((x{8}){1,5}|(x{64})+|xx?|xxxx)$ 2014-01-12 23:07:15 sneakyruds (R)
  31 ^(((x|x{16}|x{256})\3?)\2?)\1?$ 2014-02-12 16:09:28 Davidebyzero (GH)
  17 ^((x+)(?=\2$))*x$ 2014-02-21 21:30:06 Davidebyzero (GH,RG)
  17 ^(?!(x*)(\1\1)+$) 2019-02-05 Grimy (GH)
Long count 14 almost certainly the 14-scoring one below 2014-01-07 12:27:38 timloh (RG~) (discovery date is earlier than indicated date)
  15 ((.+)0\2[1]){8} 2014-01-15 06:28:48 abjr (GH)
  14 ((.+)0\2+1){8} 2014-01-15 12:04:50 hugetoon (GH)
Alphabetical 78 ^(?!.*(rne|eet |e.r...t|er.{6}r$))(a\S+\s)*(e\S+\s)*(r\S+\s)*([st]\S+(\s|$))*$ 2013-12-25 05:25:31 muxrwc (GH)
  46 [^et] ren|[er]( \w+)\1|tate r|a t| ae|rt r|e e 2013-12-25 15:31:12 alexandrosm (GH)
  45 [^et] ren|[er]( \w+)\1|(tat|r). r|a t| ae|e e 2013-12-25 16:26:59 alexandrosm (GH)
  41 s ren|[er]( \w+)\1|(tat|r). r|a t| ae|e e 2013-12-25 16:59:02 alexandrosm (GH)
  37 r sn|( t\w+)\1|(tat|r). r|a t| ae|e e 2013-12-25 23:45:16 alexandrosm (GH)
  36 ( .+[ts]..)\1|(tat|r). r|a t| ae|e e 2013-12-27 21:56:51 bbarry (GH)
  33 ( .+[ts]..)\1|(tat|r). r|a t|e .r 2013-12-30 00:22:58 alexandrosm (GH)
  23 .r.{32}r|a.{10}te|n.n.. 2013-12-31 17:04:35 alexandrosm (GH)
  23 almost certainly the above 2014-01-07 12:27:38 timloh (RG~) - probably copied alexandrosm's solution
  54 ^(?!.* ((.*)t.* \2[es]|(.*)s.* \3[nr]|(.*)r.* \4[en])) 2014-01-13 00:25:24 dcwarwick (GH)
  43 ^(?!.*( .*)(t.*\1[es]|s.*\1[nr]|r.*\1[en])) 2014-02-15 04:48:38 Davidebyzero (GH) - optimization of dcwarwick's solution
  22 [unpublished] 2018-02 ≈ LLB (RG)
Powers 2 19 ^((x+)\2(?=\2$))*x$ 2014-04-25 22:45:17 Davidebyzero (GH,RG)
  22 ^(?!((xxx)+x|xx|)\1*$) 2014-09-18 03:05:37 muxrwc (GH)
  21 ^(?!(x(xxx)+|xx)\1*$) TH (RG), Davidebyzero (GH,RG)

Robust solutions

Level Length Regex Domain Date Credit
Plain strings 3 foo ^[A-Za-z][a-z]*$
Anchors 4 ick$ ^[A-Za-z][a-z]*ick[a-z]*$
Ranges 8 ^[a-f]*$ ^[a-z]+$
Backrefs 9 (...).*\1 ^[a-z]+$
Abba 17 ^(?!.*(.)(.)\2\1) ^[a-z]+$
A man, a plan 14 ^(.)(.).*\2\1$
  40 ^(.?)(.?)(.?)(.?)(.?)(.?).?\6\5\4\3\2\1$ ^[a-z]+$*
Prime 14 ^(?!(11+)\1+$)**** ^11+$ 1997-10-22 18:17:07 Abigail (P)
  - ^(11+?)\1+$***** ^11+$ 1997-10-23 17:53:10 John L. Allen (P)
  14 ^(?!(xx+)\1+$) ^xx+$
  15 ^(?!(xx+|)\1+$) ^x*$*** 2014-03-13 14:12:05 Davidebyzero (GH)
  - ^1?$|^(11+?)\1+$***** ^1*$ 1997-11-19 Abigail (P)
  16 ^(?!(xx+)\1+$)xx ^x*$ 2014-03-13 14:50:18 teukon (GH)
  18 ^(?=(xx+?)\1*$)\1$****** ^x*$ 2018-12-07 Davidebyzero (GH)
  18 (?=(x(x*))\1+$)\2^****** ^x*$ 2019-04-21 Grimy (GH)
Four 11 (.)(.\1){3} ^[A-Za-z][a-z]*$
Order 54 ^a*b*c*d*e*f*g*h*i*j*k*l*m*n*o*p*q*r*s*t*u*v*w*x*y*z*$ ^[a-z]+$
Triples 107 ^([0369]|[258][0369]*[147]|([147]|[258][0369]*[258])([0369]|[147][0369]*[258])*([258]|[147][0369]*[147]))*$ ^.+$ 2013-03-27 21:49:49 joel
  107 ^([0369]|[147][0369]*[258]|([258]|[147][0369]*[147])([0369]|[258][0369]*[147])*([147]|[258][0369]*[258]))*$ ^.+$
  106 ^(?=((.*?[147]){3})*((.*?[147]|){2}))(?=((.*?[258]){3})*((.*?[258]|){2})).*$(\3\7|\4\8(?!\3|\7)|(?!\4|\8)) ^[0-9]+$ 2014-02-13 to 2014-02-25 Davidebyzero & teukon (GH) (for full history, see below)
Glob 81 ^(\*?)(\w*)(\*?)(\w*)(\*?)(\w*) .* ((?!\1).+|\1)\2((?!\3).+|\3)\4((?!\5).+|\5)\6$ 2014-01-07 10:52:43 DiEvAl (GH) - created before hard mode; didn't match the domain of hard mode
  78 ^(\*?)(.*)(\*?)(.*)(\*?)(.*) .* ((?!\1).+|\1)\2((?!\3).+|\3)\4((?!\5).+|\5)\6$ 2014-01-15 20:35:11 teukon (GH) - DiEvAl's solution modified to assume that * never occurs to the right of matches
  84 ^(.*)(\*?)(.*)(\*?)(.*)(\*?)(.*) .* \1((?!\2).+|\2)\3((?!\4).+|\4)\5((?!\6).+|\6)\7$ see below 2014-04-26 02:26:43 Davidebyzero (GH) - DiEvAl's solution modified to assume that * never occurs to the right of matches, and to match hard mode
Balance 37 ^(<(<(<(<(<(<(<>)*>)*>)*>)*>)*>)*>)*$ ^[<>]*$**
Powers 17 ^(?!(x(xx)+)\1*$) ^x+$
  17 ^((x+)(?=\2$))*x$ ^x*$ 2014-02-21 21:30:06 Davidebyzero (GH,RG)
  17 ^(?!(x*)(\1\1)+$) ^x*$ 2019-02-05 Grimy (GH)
Long count 31 ^((?=(\S*)0).{4} (?=\2[1]))+1+$ ^([01]{4}([1 ](?!$)|$)){16}$ 2014-02-25 Davidebyzero (GH)
  35 ^((?=(\S*)0).{4} (?=\2[1])){15}\2.$ ^.*$ 2014-02-25 22:33:53 teukon (GH)
Alphabetical 76 ^(?!.*\b((.*)n.*\b\2[e]|(.*)r.*\b\3[ne]|(.*)s.*\b\4[rne]|(.*)t.*\b\5[srne])) ^([aenrst]{6} ?\b)+$ 2014-01-09 06:49:57 AlanDeSmet (GH)
  58 ^(?!.*\b(.*)(e|(n|r|(s|t))).* \1(a|(?!\3)[en]|(?!\4)[rs])) ^([aenrst]{6} ?\b)+$ 2014-01-15 23:57:01 teukon (GH)
Powers 2 19 ^((x+)\2(?=\2$))*x$ ^x*$ 2014-04-25 22:45:17 Davidebyzero (GH,RG)
  23 ^(?!(x(xxx)+x?|xx)\1*$) ^x+$ 2018-12-05 Davidebyzero (GH)
  24 ^(?!(x(xxx)+x?|xx|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)

* A man, a plan - impossible in the general case, so this solution has a maximum robust length of 13 letters.
** Balance - impossible in the general case, so this solution has a maximum depth of 7 nesting levels.
*** If 1 is considered to be a prime number.
**** Included for historical purposes. Not technically a valid solution to this level since it works on 1s instead of xs.
***** Included for historical purposes. Not technically a valid solution to this level since it matches non-primes instead of primes and works on 1s instead of xs.
****** Of interest because of the implicit rather than explicit rejection of 0 and 1 as primes.

Robust solutions for Triples

Length Regex Domain Date Credit
  229 ^([0369]|[258][0369]*[147]|[147]([0369]|[147][0369]*[258])*[258]|[258][0369]*[258]([0369]|[147][0369]*[258])*[258]|[147]([0369]|[147][0369]*[258])*[147][0369]*[147]|[258][0369]*[258]([0369]|[147][0369]*[258])*[147][0369]*[147])*$ ^.+$ 2013-03-27 20:58:04 Alok Menghrajani
  107 ^([0369]|[258][0369]*[147]|([147]|[258][0369]*[258])([0369]|[147][0369]*[258])*([258]|[147][0369]*[147]))*$ ^.+$ 2013-03-27 21:49:49 joel
  ^([0369]|[147][0369]*[258]|([258]|[147][0369]*[147])([0369]|[258][0369]*[147])*([147]|[258][0369]*[258]))*$ ^.+$
  255 ^((?=(([^147]*[147]){3})*[^147]*$)(?=(([^258]*[258]){3})*[^258]*$)|(?=(([^147]*[147]){3})*[^147]*[147][^147]*$)(?=(([^258]*[258]){3})*[^258]*[258][^258]*$)|(?=(([^147]*[147]){3})*([^147]*[147]){2}[^147]*$)(?=(([^258]*[258]){3})*([^258]*[258]){2}[^258]*$)) ^[0-9]+$ 2014-02-13 07:11:40 Davidebyzero (GH)
  241 ^((?=(([^258]*[258]){3})*[^258]*$)(([^147]*[147]){3})*[^147]*|(?=(([^258]*[258]){3})*[^258]*[258][^258]*$)(([^147]*[147]){3})*[^147]*[147][^147]*|(?=(([^258]*[258]){3})*([^258]*[258]){2}[^258]*$)(([^147]*[147]){3})*([^147]*[147]){2}[^147]*)$ ^[0-9]+$ 2014-02-13 07:36:23 Davidebyzero (GH)
  227 ^((?=(([^258]*[258]){3})*[^258]*$)(([^147]*[147]){3})*|(?=(([^258]*[258]){3})*[^258]*[258][^258]*$)(([^147]*[147]){3})*[^147]*[147]|(?=(([^258]*[258]){3})*([^258]*[258]){2}[^258]*$)(([^147]*[147]){3})*([^147]*[147]){2})[^147]*$ ^[0-9]+$ 2014-02-13 09:52:00 Davidebyzero (GH)
  222 ^((?=(((([^258]*[258]){3})*[^258]*)|((([^258]*[258]){3})*[^258]*[258][^258]*)|((([^258]*[258]){3})*([^258]*[258]){2}[^258]*)|([^258]*))$)(([^147]*[147]){3})*(\6\6\9\9|\3\3\13\13[^147]*[147](\9\9|\6\6[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 14:43:43 Davidebyzero (GH)
  180 ^((?=((([^258]*[258]){3})*[^258]*))(?=((\2)|(\2[258][^258]*)|(\2([258][^258]*){2})|([^258]*))$)(([^147]*[147]){3})*(\7\7\8\8|\6\6\10\10[^147]*[147](\8\8|\7\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 14:51:01 Davidebyzero (GH)
  ^((?=((([^258]*[258]){3})*[^258]*)(.*)$)(?=((\2)|(\2[258][^258]*)|(\2([258][^258]*){2})|(\3))$)(([^147]*[147]){3})*(\8\8\9\9|\7\7\11\11[^147]*[147](\9\9|\8\8[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:08:35 Davidebyzero (GH)
  176 ^((?=((([^258]*[258]){3})*[^258]*))(?=((\2)|(\2[258][^258]*)|\2([258][^258]*){2}|([^258]*))$)(([^147]*[147]){3})*(\7\7\8\8|\6\6\9\9[^147]*[147](\8\8|\7\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:29:20 Davidebyzero (GH)
  170 ^((?=((([^258]*[258]){3})*[^258]*))(?=((\2)|(\2[258][^258]*)|\2([258][^258]*){2}|([^258]*))$)(([^147]*[147]){3})*(\7\7\8\8|\6\9[^147]*[147](\8\8|\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:36:30 Davidebyzero (GH)
  169 ^((?=((([^258]*[258]){3})*[^258]*))(?=((\2)|((\2[258][^258]*)|\2([258][^258]*){2})|([^258]*))$)(([^147]*[147]){3})*(\7\7|\6\10[^147]*[147](\9\9|\8[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:47:33 Davidebyzero (GH)
  168 ^((?=((([^258]*[258]){3})*[^258]*))(?=(((\2[258][^258]*)|\2([258][^258]*){2})|((\2)|([^258]*)))$)(([^147]*[147]){3})*(\6\6|\9[^147]*[147](\8\8|\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:52:22 Davidebyzero (GH)
  164 ^((?=((([^258]*[258]){3})*[^258]*))(?=(((\2[258][^258]*)|\2([258][^258]*){2})|(\2|[^258]*))$)(([^147]*[147]){3})*(\6\6|\9[^147]*[147](\8\8|\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:53:11 Davidebyzero (GH)
  163 ^((?=((([^258]*[258]){3})*[^258]*))(?=(((\2[258][^258]*)|\2([258][^258]*){2})|(\2[^258]*))$)(([^147]*[147]){3})*(\6\6|\9[^147]*[147](\8\8|\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 15:59:11 Davidebyzero (GH)
  156 ^((?=((([^258]*[258]){3})*[^258]*))(?=(((\2[258][^258]*)|\2([258][^258]*){2})|(\2))$)(([^147]*[147]){3})*(\6\6|\9[^147]*[147](\8\8|\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 16:02:02 Davidebyzero (GH)
  156 ^((?=((([^258]*[258]){3})*[^258]*))(?=((\2([258][^258]*)|\2([258][^258]*){2})|(\2))$)(([^147]*[147]){3})*(\6\6|\9[^147]*[147](\8\8|\7[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 16:09:21 Davidebyzero (GH)
  158 ^((?=((([^258]*[258]){3})*[^258]*))(?=((\2)|((\2[258][^258]*)|(\2([258][^258]*){2})))$)(([^147]*[147]){3})*(\7\7|\6[^147]*[147](\9\9|\8[^147]*[147]))[^147]*)$ ^[0-9]+$ 2014-02-13 16:15:43 Davidebyzero (GH)
  156 ^(?=((([^258]*[258]){3})*[^258]*))(?=((\1)|((\1[258][^258]*)|(\1([258][^258]*){2})))$)(([^147]*[147]){3})*(\6\6|\5[^147]*[147](\8\8|\7[^147]*[147]))[^147]*$ ^[0-9]+$ 2014-02-14 13:29:23 Davidebyzero (GH)
  153 ^(?=(([^258]*[258]){3})*[^258]*([258][^258]*([258][^258]*)?)?$)(([^147]*[147]){3})*(?=([^147]*))\7((?!\3)(?=([147][^147]*))\9((?!\4)[147][^147]*|\4)|\3)$ ^[0-9]+$ 2014-02-15 06:45:47 Davidebyzero (GH)
  157 ^(?=[^147]*([147]?)[^147]*([147]?)[^147]*(([147][^147]*){3})*$)[^258]*((?=.*$\1)|(?!.*$\1)[258])[^258]*((?=.*$\2)|(?!.*$\2)[258])[^258]*(([258][^258]*){3})*$ ^[0-9]+$ 2014-02-16 20:55:58 teukon (GH) (discovery date is probably earlier)
  153 ^(?=(([^258]*[258]){3})*[^258]*([258]?)[^258]*([258]?)[^258]*$)(([^147]*[147]){3})*(?=([^147]*))\7((?!\3)(?=([147][^147]*))\9((?!\4)[147][^147]*|\4)|\3)$ ^[0-9]+$ 2014-02-17 11:36:59 Davidebyzero (GH)
  145 ^(?=(([^258]*[258]){3})*[^258]*([258]?)[^258]*([258]?)[^258]*$)(([^147]*[147]){3})*(?=([^147]*))\7((?!\3)(?=(.[^147]*))\9((?!\4).[^147]*|\4)|\3)$ ^[0-9]+$ 2014-02-17 20:23:11 teukon (GH)
  ^(?=[^147]*([147]?)[^147]*([147]?)[^147]*(([147][^147]*){3})*$)(?=([^258]*))\5(\1|(?!\1).)(?=([^258]*))\7(\2|(?!\2).)[^258]*(([258][^258]*){3})*$ ^[0-9]+$ 2014-02-17 20:23:11 teukon (GH)
  137 ^(?=(([^258]*[258]){3})*[^258]*(.?)[^258]*(.?)[^258]*$)(([^147]*[147]){3})*(?=([^147]*))\7((?!\3).|\3)(?=([^147]*))\9((?!\4).|\4)[^147]*$ ^[0-9]+$ 2014-02-18 08:01:51 Davidebyzero (GH)
  ^(?=[^147]*(.?)[^147]*(.?)[^147]*(([147][^147]*){3})*$)(?=([^258]*))\5(\1|(?!\1).)(?=([^258]*))\7(\2|(?!\2).)[^258]*(([258][^258]*){3})*$ ^[0-9]+$ 2014-02-18 08:01:51 Davidebyzero (GH)
  ^(?=[^147]*(.?)[^147]*(.?)[^147]*(([147][^147]*){3})*$)(?=([^258]*))\5(?=(\1|.))\6(?=([^258]*))\7(?=(\2|.))\8[^258]*(([258][^258]*){3})*$ ^[0-9]+$ 2014-02-18 08:01:51 Davidebyzero (GH)
  127 ^(?=(([^147]*[147]){3})*[^147]*(.?)[^147]*(.?))(?=(([^258]*[258]){3})*[^258]*(.?)[^258]*(.?))\d+$(\3\7|\4\8(?!\3|\7)|(?!\4|\8)) ^.*$ 2014-02-18 12:23:02 Davidebyzero (GH)
  126 ^(?=(([^147]*[147]){3})*[^147]*(.?)[^147]*(.?))(?=(([^258]*[258]){3})*[^258]*(.?)[^258]*(.?)).+$(\3\7|\4\8(?!\3|\7)|(?!\4|\8)) ^[0-9]*$ 2014-02-18 12:23:02 Davidebyzero (GH)
  119 ^(?=((.*?[147]){3})*[^147]*(.?)[^147]*(.?))(?=((.*?[258]){3})*[^258]*(.?)[^258]*(.?))\d+$(\3\7|(?!\3|\7)\4\8|(?!\4|\8)) ^.*$ 2014-02-18 18:55:50 teukon (GH)
  118 ^(?=((.*?[147]){3})*[^147]*(.?)[^147]*(.?))(?=((.*?[258]){3})*[^258]*(.?)[^258]*(.?)).*$(\3\7|(?!\3|\7)\4\8|(?!\4|\8)) ^[0-9]*$ 2014-02-18 18:55:50 teukon (GH)
  111 ^(?=((.*?[147]){3})*(((.*?[147])?){2}))(?=((.*?[258]){3})*(((.*?[258])?){2}))\d+$(\3\8|\4\9(?!\3|\8)|(?!\4|\9)) ^.*$
  110 ^(?=((.*?[147]){3})*(((.*?[147])?){2}))(?=((.*?[258]){3})*(((.*?[258])?){2})).*$(\3\8|\4\9(?!\3|\8)|(?!\4|\9)) ^[0-9]+$ 2014-02-19 10:48:11 Davidebyzero (GH)
  107 ^(?=((.*?[147]){3})*((.*?[147]|){2}))(?=((.*?[258]){3})*((.*?[258]|){2}))\d+$(\3\7|\4\8(?!\3|\7)|(?!\4|\8)) ^.*$
  106 (?=((.*?[147]){3})*((.*?[147]|){2}))(?=((.*?[258]){3})*((.*?[258]|){2}))^.*$(\3\7|(?!\3|\7)\4\8|(?!\4|\8)) ^[0-9]+$ 2014-02-25 01:50:02 teukon (GH)
  106 ^(?=((.*?[147]){3})*((.*?[147]|){2}))(?=((.*?[258]){3})*((.*?[258]|){2})).*$(\3\7|\4\8(?!\3|\7)|(?!\4|\8)) ^[0-9]+$

Robust solutions for Powers of various bases

Base Length Regex Domain Date Credit
  0 2 ^$ ^x*$
  1 3 ^x$ ^x*$
  2 17 ^((x+)(?=\2$))*x$ ^x*$ 2014-02-21 21:30:06 Davidebyzero (GH,RG)
  17 ^(?!(.(..)+)\1*$) ^x+$ 2013-12-20 19:18:06 plby (GH)
  17 ^(?!(x(xx)+)\1*$) ^x+$
  18 ^(?!(x(xx)+|)\1*$) ^x*$ 2014-03-13 13:21:03 Davidebyzero (GH)
  17 ^(?!(x*)(\1\1)+$) ^x*$ 2019-02-05 Grimy (GH)
  3 19 ^((x+)\2(?=\2$))*x$ ^x*$ 2014-04-25 22:45:17 Davidebyzero (GH,RG)
  23 ^(?!(x(xxx)+x?|xx)\1*$) ^x+$ 2018-12-05 Davidebyzero (GH)
  24 ^(?!(x(xxx)+x?|xx|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  25 ^(?!((xxx)*(xx)\3?|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  31 ^(?!(x*)(?!(\1\1)(\1\2)*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  30 ^(?!(x*)(?!\1\1(\1{3})*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  26 ^(?!(x*)(\1|(\1{3})+\1?)$) ^x*$ 2019-02-08 Davidebyzero (GH)
  4 21 ^((x+)\2\2(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  5 22 ^((x+)\2{3}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  33 ^(?!(x(x{5})+x?x?x?|xxx?x?|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  33 ^(?!(x(x{5})+x{0,3}|x{2,4}|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  31 ^(?!(xx(x{5})*(x{4}|x?x?))\1*$) ^x+$ 2018-12-05 Davidebyzero (GH)
  32 ^(?!(xx(x{5})*(x{4}|x?x?)|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  32 ^(?!(x*)(?!(\1{4})(\1\2)*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  31 ^(?!(x*)(?!\1{4}(\1{5})*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  34 ^(?!(x*)(\1?\1?(\1|(\1{5})+\1?))$) ^x*$ 2019-02-08 Davidebyzero (GH)
  35 ^(?!(x*)(\1{1,3}|(\1{5})+\1{0,3})$) ^x*$ 2019-02-08 Davidebyzero (GH)
  6 22 ^((x+)\2{4}(?=\2$))*x$ ^x*$ 2014-02-21 21:40:31 teukon (GH)
  7 22 ^((x+)\2{5}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  32 ^(?!(x(x{7})+x{0,5}|x{2,6})\1*$) ^x+$ 2018-12-05 Davidebyzero (GH)
  33 ^(?!(x(x{7})+x{0,5}|x{2,6}|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  34 ^(?!(xx(x{7})*(x{6}|x{0,4})|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  32 ^(?!(x*)(?!(\1{6})(\1\2)*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  31 ^(?!(x*)(?!\1{6}(\1{7})*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  35 ^(?!(x*)(\1{0,4}(\1|(\1{7})+\1?))$) ^x*$ 2019-02-08 Davidebyzero (GH)
  35 ^(?!(x*)(\1{1,5}|(\1{7})+\1{0,5})$) ^x*$ 2019-02-08 Davidebyzero (GH)
  8 22 ^((x+)\2{6}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  9 22 ^((x+)\2{7}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  10 22 ^((x+)\2{8}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  11 22 ^((x+)\2{9}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  34 ^(?!(x(x{11})+x{0,9}|x{2,10})\1*$) ^x+$ 2018-12-05 Davidebyzero (GH)
  35 ^(?!(x(x{11})+x{0,9}|x{2,10}|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  33 ^(?!(x*)(?!(\1{10})(\1\2)*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  33 ^(?!(x*)(?!\1{10}(\1{11})*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  36 ^(?!(x*)(\1{0,8}(\1|(\1{11})+\1?))$) ^x*$ 2019-02-08 Davidebyzero (GH)
  36 ^(?!(x*)(\1{1,9}|(\1{11})+\1{0,9})$) ^x*$ 2019-02-08 Davidebyzero (GH)
  12 23 ^((x+)\2{10}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  13 23 ^((x+)\2{11}(?=\2$))*x$ ^x*$ 2018-12-05 Davidebyzero (GH)
  35 ^(?!(x(x{13})+x{0,11}|x{2,12})\1*$) ^x+$ 2018-12-05 Davidebyzero (GH)
  36 ^(?!(x(x{13})+x{0,11}|x{2,12}|)\1*$) ^x*$ 2018-12-05 Davidebyzero (GH)
  33 ^(?!(x*)(?!(\1{12})(\1\2)*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  33 ^(?!(x*)(?!\1{12}(\1{13})*$)\1+$) ^x+$ 2019-02-08 Davidebyzero (GH)
  37 ^(?!(x*)(\1{0,10}(\1|(\1{13})+\1?))$) ^x*$ 2019-02-08 Davidebyzero (GH)
  38 ^(?!(x*)(\1{1,11}|(\1{13})+\1{0,11})$) ^x*$ 2019-02-08 Davidebyzero (GH)

If the domain of Glob must be stated in a single regex, it would be:
^([a-z]*)\*?([a-z]*)\*?([a-z]*)\*?([a-z]*) matches \1[a-z]*\2[a-z]*\3[a-z]*\4$
However, it may actually have 4 domains:
^([a-z]*)\*([a-z]+)\*([a-z]*) matches \1[a-z]*\2[a-z]*\3$
^\*([a-z]+)\*([a-z]+)\* matches [a-z]+\1[a-z]+\2[a-z]+$ (left only)
^([a-z]+)\*([a-z]+) matches [a-z]*\1[a-z]+\2[a-z]*$ (right only)
^\*?([a-z]+)\*? matches [a-z]*\1[a-z]*$

The domains above may be controversial, as we have a limited sampling. Feel free to discuss them in this Gist.

Triples (107) DFA solution, pretty-printed:

^( [0369] | [258][0369]*[147] |
  ( [147] | [258][0369]*[258])
  ([0369] | [147][0369]*[258])*
  ( [258] | [147][0369]*[147]))*$

Triples (106) lookahead + backreferences solution, pretty-printed:

^(?=((.*?[147]){3})*((.*?[147]|){2}))
 (?=((.*?[258]){3})*((.*?[258]|){2}))
 .*$(\3\7 | \4\8(?!\3|\7) | (?!\4|\8))

Glob (84), pretty-printed:

^(.*)(\*?)
 (.*)(\*?)
 (.*)(\*?)(.*) .* \1((?!\2).+|\2)
                  \3((?!\4).+|\4)
                  \5((?!\6).+|\6)\7$
@Dinoguy1000
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@Hammad1007 See the explanations in the "Solutions" dropdowns on my Regex Golf page. If you still have questions after that, I can try to answer them for you, as long as you're more specific. =)

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