Automatas Y Lenguajes Formales Código: 301405A - 764

 

PLKQ@RVKJOJ LOFKCLOG OBK@RZO [ O JKVZOLFKO - PLOJ @VFP@GO J@ FK@LFKO BÏVKFOV, B ÏVKFOV, Z@FLCGCMÅO @ KLM@LK@RÅO XRCMROEO KLM@LK@RKO J@ VKVZ@EOV ‖  F@OJ  F@OJ BPFOROEOLMO

OPZCEOZ OPZCEO ZOV [ G@LM G@LMPON@V PON@V ACREOG ACREOG@V @V  Föjkmc> 68?:80OS=1: 

Zor`o ? - Auljoe`ltofköl 

@stujkolt`> Mr`mcrkc Ecr`lc ]kgfd`s Föjkmc> ?641?424 Zutcr> Q@RE@L ROKL@R O[OGO  O[OGO 

F@OJ j` Buforoeolmo V`tk`ebr` 2828

 

  @N@RFKFKCV O J@VORRCGGOR    O fcltkluofköl, s` j`akl`l gcs `n`rfkfkcs o j`sorrcggor `l ulo pr`s`ltofköl j` Xcw`rXcklt go fuog s` muorjorï `l pja>   

@n`rfkfkc ?> R`ogkzor ulo gål`o j`g tk`epc qu` p`rekto cbs`rvor go dkstcrko y `vcgufköl j` go t`cråo j` outöeotos y g`lmuon`s acreog`s, s` j`b` t`l`r `l fu`lto gcs cråm`l`s, gcs  pr`furscr`s y gcs jkstkltcs foepcs `l gcs qu` r`p`rfut` r`p `rfut` `sto ïr`o j`g fclcfkek`ltc (Klm`lk`råo, g`lmuon`s y mroeïtkfos, eot`eïtkfos y fceputobkgkjoj) y opgkfofköl jkr`fto j` gos fk`lfkos fceputofkclog`s. .   

@n`rfkfkc 2> R`ogkzor go pr`s`ltofköl fcl go fclf`ptuogkzofköl y `n`epgcs j`> Ogaob`tc>   `s ul fclnultc aklktc y crj`lojc j` såebcgcs. Xcr `n`e Ogaob`tc> `n`epgc> pgc> @ 5 {o, 1, f, j, `} c `g ogaob`tc bklorkc £ 5 {8,?}. @g crj`l j` sus `g`e`ltcs s` j`lceklo crj`lofköl ogaobëtkfo.

 

  Xogobro c Foj`lo> @s ulo s`fu`lfko j` ul lþe`rc orbktrorkc (aklktc) j` såebcgcs j`g ogaob`tc. Xcr `n`epgc, w 5 ofï skmlkakfo qu` go foj`lo w `stï acreojo pcr ulo s`fu`lfko j` tr`s såebcgcs j`g ogaob`tc> o, f y o. Jcs s`fu`lfkos fcepu`stos j` gcs eksecs såebcgcs, p`rc `l jka`r`lt` crj`l scl jkstkltos> ofï / foï. @g lþe`rc j` såebcgcs qu` fcepcl`l go foj`lo `s su gclmktuj, y s` r`pr`s`lto pcr Ww

G`lmuon`> `s ul subfclnultc fuogquk`ro j` foj`los j` @*. Xcr `n`epgc, gos aros`s j`g fost`ggolc scl ul subfclnultc j` tcjos gos foj`los qu` s` pu`j`l acreor o portkr j`g ogaob`tc dobk-tuog, gos g`tros `sp`fkog`s (ÿ, ï, ...), y gcs skmlcs j` pultuofköl. X`rc toebkël ggoeor`ecs, pcr ologcmåo, g`lmuon`s o fclnultcs fcec pcr `n`epgc `g j` gos foj`los  bklorkos qu` `xpr`sol ul lþe`rc por. Pl pcskbg` g`lmuon` `s oquëg qu` lc fcltk`l` lklmulo foj`lo c fclnultc vofåc, qu` s` r`pr`s`lto pcr 8. Kepcrto jkstklmukr `ltr` `st` y ` qu` `s ulo foj`lo y fcec tog pu`j` `stor `l ul fclnultc. G`lmuon` r`mugor> Og Og  g`lmuon` m`l`rojc pcr e`jkc j` e`jkc j` ulo mroeïtkfo r`mugor, scl oqu`ggcs g`lmuon`s fuyos foj`los `stï acreojos pcr go fclfot`lofköl j` såebcgcs, `l gos fuog`s lc doy r`gofköl `ltr` ulo port` j` go foj`lo y ctro port` j` go foj`lo.   Q`ecs qu` ulo mroeïtkfo r`mugor c j` tkpc 6 `s oqu`ggo mroeïtkfo jclj` gos r`mgos j`  prcjuffköl skmu`l go skmuk`lt` `strufturo> O→ uB c O→ u jclj` u∄ Z* y O,B∄ Q @xpr`sköl r`mugor> Plo `xpr`sköl r`mugor lc `s eïs qu` ul tkpc j` lctofköl eot`eïtkfo poro r`pr`s`l-tor g`lmuon`s. Gcs fclnultcs r`pr`s`ltobg`s e`jkolt` ulo `xpr`sköl r`mugor r`fkb`l `g lcebr` j` fclnultcs r`mugor`s. Oulqu` go j`aklk-fköl j` `stcs fclnultcs lc por`f` muorjor lklmulo r`gofköl fcl go acreo `l qu` s` kltrcjun`rcl gcs g`lmuon`s r`mugor`s, gg`mor`ecs o go klt`r`solt` fclfgusköl j` qu` `stoecs dobgoljc `xoftoe`lt` j` gcs eksecs cbn`tcs. Gos `xpr`skcl`s r`mugor`s, qu` utkgkzor`ecs poro foroft`rkzor gcs fclnultcs r`mugor`s, pu`j`l s`r j`aklkjos r`furskvoe`lt`. Vk `sfrkbk-ecs G(r) poro `g fclnultc j`lctojc pcr ulo `xpr`sköl r, `ltclf`s>

Ô `s ulo `xpr`sköl r`mugor qu` j`lcto `g g`lmuon` vofåc (G(Ô) 5 Ô)9 `s ulo `xpr`sköl r`mugor qu` j`lcto `g g`lmuon` qu` sögc fcl-tk`l` go foj`lo vofåo ( G ( )

5 { })9

Vk o `s ul såebcgc j` @  `ltclf`s o `s ulo `xpr`sköl r`mugor qu` j`lcto `g g`lmuon` qu` fcltk`l` go foj`lo o ( G ( )

5 { })9

 

 

@xpr`sköl j` fclnultcs> Gcs fclnultcs s` j`lctol dobktuoge`lt` pcr g`tros eoyþsfugos. Gcs cbn`tcs qu` fcepcl`l `g fclnultc s` ggoeol `g`e`ltcs c ek`ebrcs. V` jkf` qu` «p`rt`l`f`l¹ og fclnultc y s` j`lcto e`jkolt` `g såebcgc ∄> go `xpr`sköl o ∄ O s` g`` `ltclf`s fcec «o `stï `l O¹, «o p`rt`l`f` o O¹, «O fcltk`l` o o¹.  o¹.   C* (fclnultc j` tcjos gos foj`los j` f`rcs) (C + ?) * (fclnultc j` foj`los acreojos pcr f`rcs y ulcs, `s j`fkr, @* (?8) * (foj`los acreojos pcr s`fu`lfkos j` ?8, klfguy`ljc `)

Xcr @xt`lsköl> sk @xt`lsköl> sk s` `lue`rol sus `g`e`ltcs. Fclstrukr c j`aklkr ul fclnultc pcr `xt`lsköl fclskst` `l j`fgoror tcjcs gcs `g`e`ltcs qu` gc acreol. Xcr `n`epgc> O 5 {x / x `s ul lþe`rc cbt`lkjc og golzor ul jojc fcrrk`lt`} `s ul fclnultc j`aklkjc pcr fcepr`lsköl yo qu` sus `g`e`ltcs ‗x― s` j`sfrkb`l o  trovës j` ulo prcpk`joj ‗`s ul lþe`rc cbt`lkjc og golzor ul jojc fcrrk`lt`―.   @so `xpr`sköl s` g``> ‗O `s `g fclnultc acreojc pcr tcjcs oqu`ggcs lþe`rcs qu` s` cbt`lmol og golzor ul jojc―.  Jot` fu`lto qu` go aros` `sfrkto `ltr` gos ggov`s ({...}) `stï `l sklmugor y, skl `ebormc, s` g`` `l pgurog. @s` fclnultc, `xpr`sojc pcr `xt`lsköl, `s O 5 {?,2,6,:,0,1}. Xcr klt`lsköl> Fclstrukr c j`aklkr ul fclnultc pcr klt`lfköl fclskst` `l j`fgoror fuïg`s `g`e`ltcs j` ul fk`rtc fclnultc scl s`g`ffkclojcs. @stc s` gg`vo o fobc pcr ulo prcpk`joj c pr`jkfojc X(x). {x ∄ J|X(x)} {x ∄ R| − 2 7 x} ‗Zcjcs oqu`ggcs lþe`rcs r`og`s qu` scl eoycr`s qu` -2.―  Xogobro lugo c vofåo ʌ> @g fclnultc vofåc `s `g  `g fclnultc qu` lc fcltk`l` lklmþl `g`e`ltc. `g`e`ltc. Xu`stc qu` gc þlkfc qu` j`akl` o ul fclnultc scl sus `g`e`ltcs, `g fclnultc vofåc `s þlkfc.   @g fclnultc vofåc tk`l` gos skmuk`lt`s prcpk`joj`s m`l`rog`s>   @g fclnultc vofåc `s þlkfc> jojc jcs fclnultcs skl `g`e`ltcs, oebcs scl kmuog`s. kmu og`s. (@stc nustkakfo dobgor j` "`g fclnultc vofåc" y lc j` "ul fclnultc vofåc"). @g þlkfc subfclnultc j`g fclnultc vofåc `s ëg eksec>

@g lþe`rc j` `g`e`ltcs j`g fclnultc vofåc (`s j`fkr, su lþe`rc su lþe`rc forjklog) `s forjklog) `s f`rc9 `l  portkfugor, `g fclnultc vofåc `s ul fclnultc aklktc>

 

Cp`rofköl r`mugor`s - Plköl> Go ulköl j` jcs g`lmuon`s r`mugor`s `s ctrc g`lmuon` r`mugor. V` utkgkzo go cp`rofköl j` ulköl j` fclnultcs9 oså, poro `g ogaob`tc V 5 {x, y} sk G ? 5 {x, xy} y G2 5 {yz,yy} `ltclf`s su ulköl s`rï G ? Ä G2 5 {x,xy,yz,yy }. Xoro ecjkakfor gcs jkomroeos j` trolskfkcl`s j`b`r`ecs fcls`mukr qu` s` voyo o ulo u ctro j` gos `strufturos crkmklog`s, p`rc skl e`zfgorgos (sk s` e`zfgol, s` ojektkråol foj`los qu` lc p`rt`l`f`l og g`lmuon`). Xoro `ggc fcm`r`ecs gcs jkomroeos crkmklog`s j` gcs jcs g`lmuon`s. V` jkbuno ul `stojc lu`vc> Cp`rofköl r`mugor`s - Fclfot`lofköl> Go fclfot`lofköl j` jcs g`lmuon`s r`mugor`s `s ctrc g`lmuon` r`mugor. V` fclfot`lol ulo foj`lo j`g prke`r g`lmuon` y ulo foj`lo j`g s`muljc. Fcl G? y G2 olt`rkcr`s go fclfot`lofköl (qu` s` j`lcto ¸) s`rï G? ¸ G2 5{xyx,xyy,xyyz,xyyy}. Go fclfot`lofköl lc `s fcleutotkvo (G? ¸ G2 » G2 ¸ G? ). Fcm`ecs gcs jkomroeos crkmklog`s j` gcs jcs g`lmuon`s> o.  V` jkbuno `g jkomroeo crkmklog j` G?   b.  j`sj` fojo `stojc j` of`ptofköl j`g jkomroeo j` G ? s` jkbuno ul orfc dofko fojo `stojc G2 qu` s`o `g j`stklc j` ul orfc j`g `stojc klkfkog j` G 2 y s` rctugo fcl `g eksec j` såebcgc f.  J`nor qu` gcs `stojcs j` of`ptofköl j` G? gc s`ol sk `g `stojc klkfkog j` G 2 toebkël gc `s. Cp`rofköl r`mugor`s - @str`ggo j` Ig``l` > Go `str`ggo j` Ig``l` j` fuogquk`r g`lmuon` r`mugor toebkël `s r`mugor. V` foroft`rkzo pcr qu` s` utkgkzo scgc ul g`lmuon` `l g`lmuon` `l gumor j` jcs. V` gcmro acreoljc tcjos gos fclfot`lofkcl`s j` f`rc (foj`lo f`rc (foj`lo vofåo) c eïs foj`los j`g foj`los  j`g g`lmuon` qu` s` oepgåo. Go cp`rofköl s` r`pr`s`lto fcl `g ost`rksfc suproåljkf` ( * ). Fcec s` vkc og prklfkpkc j` `st` oportojc, go foj`lo vofåo, g, lc s` fclskj`robo fcec ulc j` gcs bgcqu`s j` acreofköl j` g`lmuon`s, y `s pcrqu` s` m`l`ro o portkr j` Á pcr e`jkc j` go `str`ggopcskbg` j` Ig``l`9 vofåop`rt`l`f`r p`rt`l`f` oo Á go *`str`ggo j` Ig``l` j` }. fuogquk`r g`lmuon` y pcrgogcfoj`lo toltc j`b`  y, pcr toltc, Á**5{g Xoro ecjkakfor `g jkomroeo j` trolskfkcl`s, s` fcm` `g jkomroeo> o.  V` oÿoj` ul lu`vc `stojc qu` vo o s`r `g j` klkfkc  b.  @st` lu`vc `stojc klkfkog toebkël gc eorfor`ecs fcec j` of`ptofköl (poro qu` oså  pu`j` of`ptor go foj`lo vofåo) f.  Xcr fojo ulc j` gcs orfcs qu` doy j`sj` `g `stojc klkfkog crkmklog dofko ctrcs (pu`j` s`r `g eksec), s` jkbuno j`sj` `g lu`vc `stojc klkfkog ul orfc dofko `g `stojc j`stklc j`g orfc fcrr`spcljk`lt` `l `g jkomroeo crkmklog y s` `tkqu`to fcl `g eksec såebcgc j.  J`sj` fojo `stojc j` of`ptofköl s` jkbuno ul orfc pcr fojo ulc j` gcs qu` sog`l j`sj` `g `stojc klkfkog crkmklog dofko ctrcs (pu`j` s`r `g eksec). @st` sog` dofko `g

 

`stojc j`stklc j`g orfc fcrr`spcljk`lt` qu` sogåo j`g `stojc klkfkog `l `g jkomroeo crkmklog y s` `tkqu`to fcl `g eksec såebcgc. `.  V` qukto go foroft`råstkfo j` klkfkc j`g `stojc klkfkog crkmklog. Cp`rojcr> @l gos fclsugtos, gcs ost`rksfcs (*), pultcs (.) y skmlcs j` klt`rrcmofköl (3) s` fcepcrtol kmuog qu` `l ]kljcws. @g ost`rksfc (*) r`pr`s`lto fuogquk`r lþe`rc j` foroft`r`s. @g pultc (.) r`pr`s`lto `g aklog j` ulo foj`lo y `g skmlc j` klt`rrcmofköl (3), fuogquk`r forïft`r kljkvkjuog. Fuogquk`r forïft`r, `xf`ptc `g ost`rksfc (*), `g pultc (.), `g skmlc j` klt`rrcmofköl (3) y go  borro v`rtkfog (|), fcklfkj` j` eol`ro pr`j`t`reklojo fclskmc eksec. Gos `xpr`skcl`s r`mugor`s pu`j`l klfgukrs` `ltr` fcekggos (" ") j` op`rturo y fk`rr` y j`b`l klfgukrs` `ltr` fcekggos sk fcltk`l`l ul `spofkc c porëlt`sks j` fk`rr` ( ) ) Xr`f`j`lfko j` gcs cp`rojcr`s> Fcec fcl ctros ïgm`bros, gcs cp`rojcr`s j` gos `xpr`skcl`s r`mugor`s tk`l`l ul crj`l j` ‗pr`f`j`lfko― pr`aknojc, gc qu` skmlkakfo qu` s` oscfkol fcl sus cp`roljc `l ul j`t`reklojc crj`l. @g crj`l j` pr`f`j`lfko j` gcs cp`rojcr`s `s `g skmuk`lt`>  ?. @g cp`rojcr ost`rksfc (*) `s `g j` pr`f`j`lfko eïs ogto. @s j`fkr, s` opgkfo sögc o go s`fu`lfko eïs fcrto j` såebcgcs o su kzquk`rjo qu` fclstktuy` ulo `xpr`sköl r`mugor bk`l acreojo.  2. @g skmuk`lt` `l pr`f`j`lfko `s `g cp`rojcr j` fclfot`lofköl, c ‗pultc―. J`spuës j` opgkfor tcjcs gcs cp`rojcr`s * o sus cp`roljc, opgkfoecs gcs cp`rojcr`s j` fclfot`lofköl o sus cp`roljc. @s j`fkr, tcjos gos `xpr`skcl`s yuxtopu`stos (ojyof`lt`s skl lklmþl cp`rojcr `ltr` `ggos). Jojc qu` go fclfot`lofköl `s ulo cp`rofköl oscfkotkvo, lc kepcrto `l quë crj`l s` r`ogkf`l gos suf`skvos fclfot`lofkcl`s, oulqu` sk doy qu` `g`mkr, gos opgkfor`ecs  pcr go kzquk`rjo. 6. Xcr þgtkec, s` opgkfol tcjcs gcs cp`rojcr`s j` ulköl (+) o sus cp`roljc. Jojc qu` go ulköl toebkël `s oscfkotkvo, j` lu`vc lc kepcrto `l qu` crj`l s` gg`v`l o fobc, p`rc supcljr`ecs qu` s` fogfugol `ep`zoljc pcr go kzquk`rjo.   @l cfoskcl`s lc s` j`s`o qu` ulo `xpr`sköl r`mugor s`o omrupojo s`mþl go pr`f`j`lfko j` gcs cp`rojcr`s. @l jkfdc fosc, s` pu`j` `epg`or porëlt`sks ( ) poro omrupor gcs cp`roljc j` go acreo qu` s` j`s``. Oj`eïs, lulfo `stï j` eïs `lf`rror `ltr` porëlt`sks gcs cp`roljc qu` s` quk`rol omrupor, klfgusc oulqu` go omrupofköl j`s`ojo s`o go pr`vksto pcr gos r`mgos j` pr`f`j`lfko. 

 

R@A@R@LFKOV BKBGKCMRÏAKFOV  dttps>//skt`s.mccmg`.fce/skt`/wkikujcfsftoga/dce`/vkskcl-j`-gos-`xpr`skcl`s-r`mugor`sy-g`lmuon`s-r`mugor`s/`xpr`skcl`sr`mugor`s#>~>t`xt5Fcec%28fcl%28ctros%28%F6%O?gm`bros%2F%28gcs,cp`rol jc%28`l%28ul%28j`t`reklojc%28crj`l.&t`xt5@g%28skmuk`lt`%28`l%28pr`f` j`lfko%28`s,fclfot`lofk%F6%B6l%2F%28c%28%@2%48%;Fpultc%@2%48% ;J..  ;J dttps>//bkbgkct`fovkrtuog.uloj.`ju.fc/gcmkl3urg5dttps>//s`orfd-`bsfcdcstfce.bkbgkct`fovkrtuog.uloj.`ju.fc/gcmkl.ospx3jkr`ft5tru`&jb5lg`bi&OL56?4862&go lm5`s&skt`5`dcst-gkv`&`bv5@B&ppkj5ppSFcv`r   lm5`s&skt`5`dcst-gkv`&`bv5@B&ppkj5ppSFcv`r dttps>//bkbgkct`fovkrtuog.uloj.`ju.fc/gcmkl3urg5dttps>//s`orfd-`bsfcdcstfce.bkbgkct`fovkrtuog.uloj.`ju.fc/gcmkl.ospx3jkr`ft5tru`&jb5lg`bi&OL56?4862&go lm5`s&skt`5`dcst-gkv`&`bv5@B&ppkj5ppSFcv`r   lm5`s&skt`5`dcst-gkv`&`bv5@B&ppkj5ppSFcv`r dttps>//bkbgkct`fovkrtuog.uloj.`ju.fc/gcmkl3urg5dttp>//s`orfd.`bsfcdcst.fce/gcmkl.ospx 3jkr`ft5tru`&jb5`jsbos&OL5`jsbos.12?1?::8&golm5`s&skt`5`js-gkv`&sfcp`5skt`   3jkr`ft5tru`&jb5`jsbos&OL5`jsbos.12?1?::8&golm5`s&skt`5`js-gkv`&sfcp`5skt` dttp>//djg.doljg`.l`t/?80;1/?8:=8 dttp>//djg.doljg`.l`t/?80;1/?8:=8