Báo cáo khoa học: "NATOMAL LANGUAGES" potx

NATO~AL LANGUAGES AND THH CROMS[Z KIERARCHT -~ndr;a Korna£ InstLtuta o~ LIn~slstlc~ Rungsrlas Academy e~ ScLmncms Budapest• PeCaN° 190 H-1250 H~naary ABc~]~ACT The central claim o~ the p~per is that NL 8trlngsets ere rsgul~r° ~hz~m lndspmmdent ~rKuments ere o:~Jerad In ~•vor o ~p able posi el.n: one based on parsimony conslderat lens 9 one employing the ~(cCullo~h Pltts (1943) eode~ o~ nsuruns: end a purety linguistic one. It |s posslhle to derive exptXcJt UPl~r bounds • or the number o~ (live) states In KL mcceptors= the results show that ~lnlts state HL parsers can ha Implemented on present day computers. The positlcn o~ HL strlngssts within the rmi[ular t,,-lly Is ale. Investigated: It is prOVed that NLs are counter £rse• L~t not locally testable. The quest Ion whet her the grammes ical 8ententes o~ nn tuz~ ~L l•nKu~Eos ~orm regular (~pe 3)• context tree (Type ~)~ context sensitive (Type 1)• or recureiwely enumerahle ( Type 0 ) am te ham been subJect to much discussion ever mince Lt yam posed by Chom8 k~ In h18 seminal 1956 paper. However9 there somme to be little &aresnent an.mE the li natLtstm concerned wlth the :~eo~rnphic e posit1., of natural languages (NLs): tar instance gelch (lS6S) claims NLs to be ~lnltm state (Type ~)• white ~(etthews (197~) argues that they ere not .oven rsours~ve17 ecums~bLs. PuI~Lum and O•zder ( |~92 ) have demonstrated that the -standard ~jU[3L~=tI~; &r~uments aK~lnst the context ~emenmss o~ nntural Ten,sages ere /sl~Leclous ~ the7 did not oons£der • howe~er • the me~_~ I n~ argusant o~le red b7 ~iatthews. In Section I of thls paper I wilt brLe~Ly out~.Lne and chal~Lenge thin &rgument9 ~nd In Section 2 I will nrliue In ~evor st geichWa position. The c~&Im that NLn arm Type 3 ham several implicat|cas ~or ~InBuletlc (math)the.t7: theme wilt be discussed In ~ectloa 30 The paper preauppoaes some tam£ llsrl ty ~lth the ]~asI c aot Ions end notations o~ terns[ lmnB~ge theory: when no specJtlc reference Is given• the reader walt land a ;root both In Sol.men (1973) and H•rrLaon (1~7~) qhe'eztanaj~J1&L vies o~ ontura~ tangumges. i.e. the ldent~L~lcatl@n 05 NL8 with the set- ot their greunme tl ca[ strings (sentenced) ~aJ acmes Jme8 regarded an 1des cbar&cterLstJLc st generative 1L©gulstlcs. Since ~t ~ss Chemak) (1957:1~) who first made th~J view exptlcit • t~Ss Ls cot shelly unjust= yet It Is quite clear that the ~me £~m& w~a Implicit In much of the eork o£ the a tTucturalist Foaled. 1 In 1sot• tits 8diacovsry procedures e developed b3P tt~m mtr~ture~lsts in order to arrive at • ¢oJLnolma dascr|~tl@u (irasaar) ¢~ a NL ~s~m • set ot utterances (corpus | were aLthout e~mptLo~ based on the asnumpt2on that net£yo speakers @t t~e 18eauaie ere capable 0£ JudM-InE the Brsematlcatlty at otte~nces p~mentmd to them. Although theme pro cme£tsr om area by end 1argot Sta©tJLc•L ( empirical ) and eechenical (alger[rialto)• their presentation already |awe[veer s cirt•in oecunt of ldeelizatJ@n. Per £nmt nnce9 it Is o]~v i .us that m8 tlvm mponKo.r s themaelLve a ut t • r ungt~JnmstLcsL sentences from t~me to time• and JLt LJ elan clear t~st t~.ey can wnderstami (p~rss) sentences that ere not ntrIctLF Sarmaaat [cal ~. Nevertheless• theme met hods work quite welt in the ect~L p~ctlce at NL description9 end the atructtu, eLJ~st methodoloay has often ~een compax'ed to that oi chaslstryt physics9 end cabot ~tu~a~ No,encase 2 M~ttbmws (1979) has casted doubts on the :[u~•amnt• 1 ~ssumptlon o]~ these procsdu~en: be ctaima that native speakers are Ls ~nct ~iGIIJ;~ • to Judge the fi~" ammos I c~L£ty o~ material ~reeeuted tc /home The relevant part ot hls argumentntJLon Ls. reproduced holes: 1) See ooM. .DeC 4 In E~oomtle~d 1926~ or EarrLs Ibm66 cb 100 2) See eoKo C~-rro~l 19539 Levi-Strauss t958 cho 2 .1 #Consider (1) and (2). T~ nstLve speakers instant Late ( I ) the canoe fine. ted down the rJLvmr n ask (2) the editor authors the newspaper hired ~iked tauEhed an e~fectlve procedure In thmlr classification of sentmnces, the: presumably the cl~8si~tcatnn of (1] and (2) 8hound not depend on thnlr ponitLnn tn a tint o~ teat , sentences that aXec Ln¢tudmn sentences similar tn (3) and (4)0 (3) the man (that wen) thrown down the stairs died (4) the adLtnr (whom) the suthcrn the newspaper hA~ed tlkmd tan~hed b~ In fact It does. (1) sad (2) uitl typica~ly be c~sstfled me unare~maatAcal l~' they precede mente~en si altar to ( 3 ) and (41~ ]~t ~p'ammatlcat If they ~oltou theme Such cases are q~lte commons n (p 212 ) Moreover, wt her e |a ¢nnaldereh le empirical e~ldencn to eUi;Eeat that native speakers emptny 8 hat t ez~r nt heuristic strategies when p~nLn8 and ctannl ~y in8 sentences. ~heXr ratlance on such mtrsteEiem does not preCtu~e thnir ha~in8 ayaltabte to then an e~gectl~e procedure for deciding membarshlF 1o their tanBuaile; hown~er~ An the abncmnca n~ emp~rLcat evidence for much a procad~ra9 we are certainty sat required to poo~utate |to existence, n (p 213) From ShAm• Matthe~n coActuden thai Putnam (10~1) was not Juan iliad In appsatln8 to Chu~h.•n themln In order to show that I~LS are rec~raiwa= ~or i~ native speakers have no o~Zect|~m p~o~edura ~nr decl(LL n~ memhernhAp in thn set n.~ grammatical, sentences• then there is no tZuarantee that such pro~edur~ exists. But iS it reat~y the came that the ab~ttnr~ nf heuristic procedures n employed ]=~ native speakers ~a~ls outside the scope of ChurchVs them|s? Watt- cnn£1~med natural taws 3 are usualty taken to ha uni~ernatty vatld ~ It is unctemr why sboutd Churches thesis he an ex c~t ion to Shiny sad )tatthews of~ern no e~ldence tn corrnbnrata his ~lew8 on this point. Putnam Vs orlllin at aripzment derives Lts etren~zth trom Church ~m theelse I~ NLs are not TyFe 01, then the heuristic stratevLes o~ native speakers vLtt he £ nat ancen o f precAm ety that sort of p~oceduren that Churches thesis predicts not to exist: on the one hand• they are 'intuitively ef~ective~• and on the other hand• they are not ~rnrtnE oomp~tabte. The phenomenon obnnrved by Uatthewst namely that native a~eakers can ha c@n:ad Into a~=cnptL~ (or reJectlaK ) sentences has LittLe to do wlt~ the racurslvenase cf the bat tary o2 heuristics they em];lcy : rater, 11 caLLs the estnnslonal vies of tang~aSa £n q~antlos. ~he Fru~len Is a sethQdnLcqKAcaL nnn: 1~ NLa ore defined to |:e sets ~ Ir~aticat sen tenons • how can nna tat potent is1 eleuects for seabarsbLp~ ThAn prnbtem becomes psrtlcQLar Ly acute In hnrdert ins canes (such ~ { 1 4 ) eL:ova)• asd :lcr t~e |lnguAat who santlm to c~eck the FradLctAona o~ his Era-mar it matters hut tAttLe that m~ch du~ lcum sentences are (statisticaLLy) infrequent. The euLast way to scene this problem J~ to ~JLve up the assum~tlon that I rnm~tA~lLLty ILl a yes/no question: e desPnl o~ ~rammet Jcatnesa* can ~e Lntrnd~ced (see e.g. C~OeBby 1961) and HLe can be tz~ateci as ,graded (or e~en tummy ) mate. ThJ~ approach• ~.ceevsr, can o,nly he 8ppt£ ed in t he study cf ldiolects ( lanEs&flea n~ isdivlduat speakers )• hecaL~se there ~a no way to arrive at n iradad sat that :111 refract t~e sue ¢~ lsdivAdu L npL nJLnne In • reanoos~l.y faith~L manner 0. Supposal ~or Instance9 that ve ha~e three speekarst 1~ 1~ and Z, sad each of them cL&JmLLA the sentences a• ~ acd c consistently (t~.at Is• 1~ ha ~refers a to h mad b to c~ .then he prefers 8 to c, etc.). Now, LZ ~or s~eaker X a)~>¢, for Y 2)c)as an~ ~or Z ¢)e>h, then the aaJuzlly ~:efnrm 6 to b,. b tn c~ And c to a; In other s~a, the *BenernL opinAnn ' ~e incnnm A~t~t ( son transitive). The ~Sosa£hL ti ty theorem s o~ Arrow ( 1950 ) sakes L t clear that the ezampLe [8 typicaL: ~ader vary sisera | ccndltlcc~• 1here Lm ~AnpLy no sa~ to 8~Bre~ate ~raded mats Ln n~G~ a manner t~.at the (partial) orderAn~e .imposed ~ the Individual iradat£on~ are preserved. Therefore9 the tdes~eee n~ ~ip~m.satlcalnesa j a~proach e~st ~e raLsk[Mad, to the, study n~ Jdiolects in as~ ¢&~n ~ most tlnGul ate ~ howe~er • reject At entirety .(see Newneyer l~SO oh. ~.5*2, 5.7.1 )* ~an/no ~nmmat Jcsllty ~udgsents9 cn lha- other " h~d,. show renarkably littTe vartatLon from speaker to speaker An any IlV~ ipn~b ¢oanunity9 and It Is thls i£~~ ',',',',',',',',~ ~ ~ (c~e ltkcnen |~8|) tibet Jt~ltl'~eS t~.e as~i~Jca~ stud~ cf 8dLa, L~l~s* and- e~en ,tansuaGe n e. But I f latthan LI rAibt9 .and native speakers o~s unable to acLema.ity any sentence ever l~.e • ccabuL~r a~ their L~iumga as -eAthe.r Krma.tlca1-or nngrmamatlcat" (p 211 )• t~n A~trasuhJectlve tenta~A lXty ! ~ • mm 2 ] Par ~ape~ent notivaton of Churchl8 . thesis, see i.e. Saner: 1967: oh. 1.7 2 vLLt be lmpomalbtn to &r.hIn~e • The question in: what makes the nntlwe a~eaber Ln~ons£stent7 Zs Matthet8 ° exmmp~Le9 there can be 7,1ttts doubt that the cause o~ the Lnoonslstonc7 ls the te~t ~ : t~e spmakerts tlnauIstLc Intuition In not the souse be~ore and n.~ter reading sentences ( 3-4)0 ~hLe source o~ lncocnIstoncy can be eliminated fairly osnITy: 1~ the sentences ere presen ted Ln a I~ ndom manner (pre~teraJ)~y~ :Lth s~t~Xer n sentences among them )~ then no ncuna prowl dad by the context o1 c~assl~Icat|on n (p 213) wiLT be preach to Ha tur~Lt y, L 1 nBul st LcsL L y relevant experiments w[~.~L have to central nany other factors (~oe nell* Greenbnum and QuArk 1970)9 but as ~e shaLL aee~ there Is on need to dLsctus8 these LndL~JLdually. Pros the paler o~ lntrasubJ e©t,l~e teot&bl~ityt It cnn be ~oLy nald them weLT deeIaned oxper£ments usuaLLy provide highly consistent dote (e~en in the east at borderL 1no sent ences ), end the extenslonat y[~ oI~. NLm can be eeJntai.ned on an empirical baals as ~nLL. The actual sets desLanated en NL8 witL9 st leant to s cereals extentt depend on the choice e~ experleenta~ technique ~ but any ~.LJs d experimental method can ]be thought oJ~ 'on an al _~or| thm ~gr dec idlng q~ent loom e~ membership . J~ ~he sic[ o~[ ~ hull~la ~.1 Since the exletlnj ozporJnon tot methods can l:e replaced l~r (Interactive) computer prajraem9 the question boils down to this: Is ~ TutAng suschlnn e|th • human oracte more powor~'~tt than one with a TU~'|Og machine steePLe7 ]~ CbtlrchWe them|me the an~we r An negn tI ~e 9 nnd an ~[urLng e&chlnes wi th recurs lee eric lea s re an more powerlh~ than Turlnli machines eithout oracle (see Co8- RoGers [967 oh. 9.4)t 1~s muust be rec~relye. Notice9 that this time ot reasoning Is independent o~ the particular choice o~ experimental technique, or what le the same9 O~ the procLie denial tioc o~ |(ICe Th/s 18 a ¢onseq~en.ce ol the ~act that the experiment at methods tamed Ln empirical SC Lances ( |ncLudl nj TinGs|at 1c8 ) hardT7 merle thls name unlearn they are weLL- de~Aned and VmechanicaL° to such an extent that their atgeritheizetlon posen no real problems. ( ]For Instance ~ the procedure outlined above does not sa~e c fuel 8~L reterence to random sequences: the 'rnndontzatlnn ~ o~ lest sentences can he carried Out with the aid o~ ~seudorand~a sequences generated by Turln8 machine. ) This As not to say that introspective evidence or lnt~ltIon plays no role In Llnauist los ( or In dgener~L 9 In the development of science ) ~ but questi@ee 4) For the definition o~ orsoLes~ see ease Ro~ere 1967 oh. 9 concnrnL~ the pea Jr/on e~ natural 18 e~gm e Ln the Chomsky hL er archy can hardly be meem~Lnitul unless we have nose de~ln£tloa oe NLe (lot, same experLseetsl sethod to teat membership) t¢ york ~Ith, ]rialto ' slate 1~ models wore tarot de~eLnped bF aockntt ( 15S5 ) • AL though ChosmJr~y- ( L957 ch 30 [ ) at tempted to dea@nntr&to the Lnadoquac7 o~ such mode~,s, eswnrnL Ll~qzt, Lmt e s advocated their use, end thn stratIt 1cat lone1 sch©ot, ¢t lin~uLmtJ~:a ( Lamb 1966 ) perslsta in ee~ laying n- £ o.rsusLL am which inl~ in essence~ equL~a-t eat to tlnlte automata (¢t* T&bLO I 0£ Eorslde '[~83 )0 &n ~b~lcb ( ~S(S ) has pointed out~ CbomnKyon demonstration It |:shed cm t~e assumption that KLe are neL/ emhedd|n|/ to J~ LEb~t£~i~ 5~ULrLt~o ~hLs a(ans~ that tl~,e /entoncnn (L-2) -and. (5 6) s~st he equally g rsmm~ t£c& L : (S) the boss editor authors ~he u walLM~il~ r hired tired hates is shed (6) the commLtte boas edltor authors the nnespsper hired libed bates ~he~ agreed'. The- ezporlmonta. (ML~or and Zsard [9649 Narks 196a)e however t do not support thls eoncLumAon= -nat |we sFeakere oi . english react to (5 6) and (7 8) the ease way s (~)- the bonn editor authors t~e • nosmpepor hired liked hates • ~u~hod curned (S) the sacra.tory ¢oenitte haee editor "-&umbers the newspaper hired Liked hat em; choArs agreed Since (7 8) aura unireaast 1ca1 i= a=y g~'ams~ o~[ ~g.1|ahn Chosal~18 nrlgLnnl deeenmtrat/on In ~ar Rrom convlnclngt and the quantJLon whether NLs are Type ~ Is st LLL opm. In £&ctt the onty way to show that 15Am are not ~ Ie to exhibit some ln~lmLte sequence ot 8rasaatJca l sen t~cen-" ~[or.tuns t • tyt the pattern e~espLiJ[Aed An (1-4~) Is not necessary tar thin• CooA-dAneted cGsstruetinne as In 5 ) EepeciaLLy the ones workl nt with camper.re. See eeg. Marcus 1964~ Church 19S0 " 6 ] Cheerily - ( 156• ) reaards ( ~ ~ } grammatical. (-~t unecceptehte) end (7 R) uaEf~m matLcaL: for the aethndnLoaical ls~TX©atLons o£ thlE.posLtlon .nee Greene (1£72)• 3 (9) I h41v41 seen Tom (tO) 1[ hove seen ;ore old Dick (tl) I hove seen Tom• Dick and Berry can be am Los8 as, we wish: t~41 grommet Loot I ty o~ •~ch sen testes 1o independent o~ the nuob41r o~ cooJunct•. Slot 1or ( rilihl~ &cd ~ot t z~curslv• | posterns non be ~ound 1o ony HLs but o~t o~ those can b41 dea~r ~bed by re~ut• t exproiolons. ~hor•~oro9 l~ 8rooeiro do lot hove t o ncc non t ~or I to r 41 tod sell ~ embedd I oBI9 the princip~Le 0 t~ 8clout L~I ¢ pus Lmony wltt point to the uLnlool toniu~ge ~osAt~ occomodatini o~or7 poslAhte ~lnlte NV- corpus end thelr reKuLor extensions. Prom tbll ~41rmg41ctlve9 the1 Type-3 ~osLty L-a more then •ul~lcient: since It coo~Lns, every ~lnIte LonEuogo a~ld 18 closed ~ndol ~ roiut•r op•rotloo•• it provides o 841serous UFpe~ bound ~o~ the ~aaJty st I~.•. A more dLre~t a~g~m41nt can he based on th41 hlolLoiLcot m~ke u];: of the human bro In: o• indivLdus~ neurone c~n bo modeS1 od by ~Lnlt 41 out elate ( |(cCut 1@ch Pitts 1943), •rid • flolt41 throe dimeniIc~ orrsy o~ such outomoto can be ~hotituted by one ~J~it• ~utaoe-to0 (see rleeno 1956)s NLe m~mt be roa~lot. A~t hough ~Lslto •tote oodelL• o~ lqLI usuotly do not c ~o Lm 41~murol ell caL reollty n (lee ch 302 ot Su~tlvoo 1980}s the obeys reoiocLng i/yam ul on ~LI;];I£ bound on the comptoxlty o~ ~lnlto outomota necessary to dooc rLbe NT.s: lincl the relevant port o~ the brain cont411om o41 more than ~0 8 eerie• sod one c•~ hem cole 102 10 3 s~atea• oon dot41rs|nlmt|c sutoelt41 with 1010 states wltl be ~!n~tfic1411~t. Slncs the ne~rotogic411 orgaaizotleo o~ the human brain-LI uotlkety to par4111sl the oc rue l orgoni zo tLon o~ the (Lnternotlzed) gramoor of native op41oker•• it iS not ourprlain8 thor the 41ppTlcotlos o~ tinK~lst|c methods give8 a mucb shorter up~41r blued : o• ~e shots sees ~inite determinist|¢ HL accepters need sot hove more then 1016 states. ~hLs eat lost Ice con be derived ~rom the Ln~41otlgatloa of the syntoct lc aonolds d4111n•d ]]7 Kiss (Fo~ the do~sition o~ syota~tlc monoidl9 see ~c~o~ahton~Pap41rt 1968 • and '1o~ a systematic expos1 tlon• see ch 3.10 of Eltaoh41r~ 19740 ) Elements o~ tb• ~nt 41ctIc mooold oorrespond to the dlsq~lhutlona~ claasej| o~ 8tructuroll•t linguistics= too strings wit1 baton8 to the same certes l~ end only if they hay41 the same diatrIhutloo~ 1.41. 1~ they can he s~bstlluted ~or eoch other In ony sentence o~ the tanEu41841 So cru418t i on. The ~AstributIonat cIaao41s ~ormod by strings o:t lonath one ~iSt he the elements o~ the ~ atphah•t; b~t I t- sho~11 d he kop~ L n mind the t these function ~s preteroio•|l los•such 41• eoch e£ them alkali ~or 41 (not notesiar Lay tinite ) clue o~ et41iooti. In e mol-pheme beus od approach9 terminals ore c411tod EeLC~IgJ~ ~K&~LO: these can be set up ~ the procedur• out110e4 lo ch 15 C~ ~srrli ( 1951}0 In o wor~oboiod oppro41ch, that let If we toke words t@ he t~.41 ulttsoto syotnctIc Coast I tuonts9 the terminals wlll 241 coLLe~ ]diKJ~JL~ ( sub )~jL~q~_~ : In either oasis ? t-he nosher oi 141rainole is ct•a~Ly ~LnLto. ;b41r~ •re o( sore thin 20 14111cnL cotiKorIia; end In •ny given HL th41ro ore Lois tb41n 300 morpheme ctass41s. ~owenrer~ ~LLy "/'orse4 words elth d/f~41rnnt I m f Tez~Lons L o~Lsea 4ILLS he'on8 to difleueemt d~atr1.~t|annl cLan•e•s and If t• - want te mo~ntalo the t41EularLt~ ut leslcoL Anmertlonv te=A©ot 41ntr141s (e.g. • 41rbl or verb •tom•) with dI f f41rnnt su kolt 41tier Lz&t Ao,s fr41sa• w J11 14111 Io d|florent lubcLo••e•. ,;r•dltIonat accounts o1 texicoL (m~b)cotoEorizotion also atLov for ov41rL oppLn& c L~ase• ( In cases u~ kaa•sLsy}- Yet the sake o~ •LmpLicltyv ! ~ill take the ~.~UL]dUUI ~tomm of •uch systems ~ ~xuJLC: t~|i ws?9 e~41ae0te like If~l or td~wr{41e wits be neilher loans ool verl0~ but eLtt be tI •ted under a s•parote ~otetior7 for tncuo v41tbos. But oven £~ v41 tika all these /Ic~orl Late-once.ors It con he safety laid that the n~mber o~ aerates41 classes do•m lot ~c•nd. - tO 3 sod the1 =ush41c 0t ll~J~=nL ~bcotoKot~le• does not •Xc4141d I-C4 io any ~voo. NI , In, ether eords• It is poosLbLe • to select, for any gI~41o ~L a Score voceJ~Lmry e ( er sorphss41 t|st) ot 104-(10 3 ) eleanora Ln Such a manner tha~ e~ery oox~ (morpheme) not oppearing In the list wiLL be d1-•t~£~utlonnLty equivalent 'ie .ono ~Lreody on it. ",This Jeans that the t~obor oil •tote• t~het tan ~e reached tn one atop ~[rom o iJL-v41n stets1 of a ~Lnite Irate NL occeptar oanoot 41xce41d 10 ~ and ¢co~ermeLys any 8|~418 state c410 ~e reached from ot moat 10 4 StOreS In on41 8t41p. ;be mtntoo ,o~ ~lnLtl automata are in one to one corronpooCauce olth the creeses oi rLdht-dLitr Lhut leo : two atrln6a c~er lh• tormLn&L vocobu~Lor7 vi1~ take t~e (oloLm~L) .outoam,ton t~ the same stote if• ~h41~ one be i~i't-~tuted ~or each other An ev41ry rL~t mLdo envlroo4141nt. AS a e~41clat ¢8•411 LT s~ouLd be o41atloned tt41t thuee l telo+l tl~tt + o not oppeo r a• lost Ia~L patti 0£ ~omticol •sat•ones wilt gl~e co! 7 o~e arose Ln the &utom41ton: the~e~ ~hero~oroe ~m be dIiregardod. "The r41ma£oLnl st~Lngu ( ~ .e. the ones that can ~s ~nJJhid 8ramuatlcatly) ha~e a ;ru;er.l~ 7] Prosmnt-~/o 7 oyntnctlclana seem to favor the Letter oppro41ch: for dlscuaoJon see ~@himi ( 1958 )t Chomsk7 ( 1°70 )s L141h41r ( 15~1). 4 pecuLler to NLm: they can mlv~ym ha fLnlmhmd with at so~t four words (ar twelve morphmNa)e 8 ~rhis Nnnu that the finm~ mrs te ~ a~ NL accoptorn can ha roached f~o~ avery Live state In at malt • aur(teethe) etepse ~here~[ora, the ~8har o~ tire mtetee La &t moat 1016 (103e)e ~- ~ma~ml0~Lg Xt mhouLd he eml~h~ized that the abave estimation Ix still Nr7 generous:. • s3mtemmtio study o~ nentmn~e acdlnsa Lu highly unLikeLy to reveal mare then 10 s different patterns Ln any glee= NL9 ead the proper ardar of magnitude amomo te be [040 If the autastaa has to accouot ~or the morpholoB~r o~ the tenSuaie el wellLt 106 20 ? orates ,eLl,1. be nacesmaS~j, this Lm• perhaps• am•aide the ctpobitittoa af present day aomputorme In any caao~ tialta automate can be 1 mp~amaoted on ~2 theoretical ( or ~=t~ml ) mode• of eorLeL computation l ilto Turi n8 m~hinon9 random &coons maahLnem e arc. to accept ~aaJuaEel Ln ~ tinge ALtb~gh native mpoaltore understand E~l~mmetica~L mrs•emcee In FJUI~ time9 tl~air per~armanca am NL accepter i m aomeehmt hindered by the fact tha.t the heotistuc algorithm., they •usa Im nat adapted ta ungramemtla•! otrinie: us~tty the7 epand momm (~LmAtmd) tame with detLberetion, end memo• imam they vest to bear the lsl;Ut airing a me~ond, tinge ~ut eves In tbie (verst) case Paaopitlon happenm In linear time• mud in thAe. raepect at Lamer9 fJLniqa automata comet Lento re•Lie•l© models of native epmsk ml-m e The imForteoco a~ thAe fact far LAn~uistic metatheo~7 should not ba ~nderos tamer ad: theme 2rmmaarka ( |lka trenn~ormatonaL iirs~mar9 see Emends l~.=) that generate ~ensumges with exponential (po~ynomLaL) reco~nltlom complexity oahe the prediction that 'these are probteno which can he malwod beth by h~mans end luring maahIne~ In a measured time9 alt~ humans sh@~inlu an. exponential (pol~mamLa~L) gain aver eachlnoa Ln the Long rune For Lnmt~ce• Lexlcal PunctionaL Grammar (see Bresnan 1983 ) melees the cream that hueoce cam solve .ca~t elm N It hard prahtema i~ lLnear time (a~e garrick I$82)~ end this in not very LLkalye On the other bond9 theme frsme~ork8 (lllte Gate, slimed P~raoe Stz'uctura Graamar~ ear Gazdar 19S2 ) that generate onty Lang~iea o~ polynamLat qimm compLexlt~ might hove memo pmycholagical 8) 1his property L- e 1lamer version a! the Depth HypothemLm (Yale 1961)o 9) Far the me~e o~ elmpLAc i t7 ][ have supposed that sentences In embedded poei.tlon ere treaLy Interchangeable• t,e, that there Is only one 8~cm~tln8 stmtoe reality; 6t. Loa~t there Is nat~lnB Iu i: to|ent d~ ¥ camplaslt:w theory that pracLude= t.bo paosibiLl ty o2 one I mpLemeatmt Los ( erie eu It I-tase ~uzici machines; o~: .~or that matter, the brain J iaLn£nG • mmALI potyoonl aL 2attar over onatbaF one ( ee 80 single-tape TuriciJ saahLnem )o A'n ether advantage of TTpa 3 NL model# ',el that .they sake tka F-rcblea ct L anipsegm maqu~a|t ia |n rateable, at ~oest lhoarotl~.LLy-e Z-t i e malt known that no el Iorlthn c~u cecJda a ha the r 8 canto~to~z-oe - ~emmar Seoerates a Bleat ceato~t £~o ~mSuage: thare£oreo If every (JnfLmdLtm) camto-3t-irec Language LS • a ~asaAbLo NL,. GburchOe thooi8 aL1L1L malta It impossAb.Le £or t~e c~.iid to acqnJre ooet let oven An same tha~ ~ava aacaa8 to a~ ereaLe (-my: .the parents) that tel~o then ubetbe~ • marine halocEa to abe 1.acEuaEo cr mate ~mre 2ore, it ta aomet imam euFpomed that the primary Linguistic data eccameL~ du~£nE la~EuaEe acq~lel qicn con•mAne not only etringst Rut the aliC~lite~ tz~e atructuram am =ella But Ite ~ e, ro- r.elUt mr I tl~o ptab~am LI melville mLtbo-t - recauraa tc that rather ItNnGo Jilt•rap•Leo= , given no upper bound an tbm ~mboz. of-atataa la the amman/eel out.moran jamb&tIDE t~e Tazguale9 it Is ScalAbLe to reconatr~t the autoietoc in 8 tlnAto nQaLbmr at queries (Maare 1S56 ), .~|mca the n~ot ol querier is at leant iO li o~ou A£. the cbltd ham access to 8 e zapz~0mmntLtA~e 1.Lepta • of 10 4 sentences thou ~esu=MI avery live meats In the automaton ~nma ASlltUJc 1881)9 end Lt le lmpomm£bLm to. make more thai tO 6 queries In • LLf£tLme• lqLI must 1arm a proper eu~mot o: re&~/L~r l~mlna~oee Z~£mct'~ the~o la reason to suFpoee that over-Jr N~ ai It be n~LD.1LJJIJi * SFacA~IcaLLy• n serial zy*z sill hel0a8 to leas NL-A~ &ad anlL 7 Af xysz is also in Lt, ~bJa la ,~bvLoue L~ ~p Le a coordinate canJ~Gt as carter c • ensnares dl ffm~-emtL at a ~etweec sin|elate d~819 trial• a~ p].u~t• the number 4 cannot ~e reduced, X£ y Am. the repented pert of some tat• or r Aght recnrslva cozelr~clJ©n (sea* a ~L~ cLeaee ), fL:e copies eLI.'L ~e Jnat as. ~rsmm~tcel as 2our co,lea eere: the converse &Lea sacrum ta hold. X~ this chara~t orJ~Jmt ~om a:l[ NLo in truer the qtadAtAo~L mode af lsniuege daecriFtSon 11 atlctAcmL, a terse As fuLLy Just|tied• hec~,ae •ewey nee contritE 1enEmiEs CaD he • uJkLt up £rom the elements a: the aT;bahai ~:e Is& ely ca taastlon end Boolean aperatAon~ (IcNaui t t on- Ps~erq IS~ l )0 Cc ~arme Ly~ am t~e ttaditiooaT ;haaotnatJLc• morphoqactAa• and syntactic daacrApt£oms oZ .~Ls used aoly ca•one•ion• ~olem• • Ante~mmctLan9 end eomettmem compLements•ion -(ic the farm of Onegatlve ¢ond£tJLom~* )~. the iaEerati~e 1so*at @~t the l~ea en~ . &rra~emeat eede~ (eat Hooka~t 19S4) deem. eat exceed thee o2 co~nter iraa 5 autonatOe It 18 allele po~mLhts tc develc~ a ~ tot the tamllL7 0t NTS: the phenomenon ot syntactic concord over unbounded domains (mhlch ~ suFpose to he present Ln o~ery I~L) ~|~LL ~u~rmntee that NLs c~nnot be ~ocatL~ ~JUI.~J * The £oL~owLni| demonstration Is based on a regular express|on used ~:y ~ttuP Gazdar ( 19S2)= coordination ( the oute%-momt El.one ) hem been added Lm order to c~mte no~ initial and non :~Lse~L elements theft ba~e to agree m/th each other. (12) ((~hich problem did ~rour protesac~ say ((she + :you) thouiht }t was uosolveJ)Lel ) + ( lthich problems did your pro~aelsor may ( ( she + you ) thouliht)~ were unsotva]:ts))4 Suppose, lndire¢ t L~ that l:ng~i sh Ls k testabLe ~or some ~lsed k, and conmider the ~011owln8 marinas: (13) ((lhlch problem did your preleesc~ sely (shel thousht you tbo~Eht )k *as unso~.wabLe ) ( lhlch problems did your pro-~melsor nay ( she tbc~kt you thouaht )k were unsotvabte))2 ( 14 ) ( ( lhJch problem did ]Four protester Say ( abe t houiht y(n/ t beuikt )k were unseLv~b ]Le ) ( VhLch problem did your pro~[smmor Say (abel the flbt you thouaht )k v~8 unsolvable ) (thlch pr~btoos did your pro~ossor say (abe thnuaht you thought)k was unsoL~obL • ) ( IbJLcb problems did your l:re~enaor ~y (elhel thoBht you thoullht )k vo~e~ unso~vabILe ) ) Apart from the order o£ the conJuncts, the only diet:terence htveen (13) and (14) Is that In the Lefts er subject- pradlc:te number agreement Is :lolmted In the ~lrst and the ~hlrd coflJ,nc~Se Thor~torme (14} IS un~r ~mmst 1 Gel, hat It hat the ISLe 8ubwords o:f tangth k (and wt"th the sane su~tlplloity) aS the ira,eroticaL ( |~ ). ~hls Cent radices o~r hypos heels that 1=niILeh was k testabLe. Hopo~u~y9 thLs sl~sciaL ponL tioc o~ NLs In the C ~N~UB ]~ h |srarc~ can ha st1 Limed in' mtrommLl nlnJ the ( oracle ) ~LRor/thms eodo~LLinB LanE~Bo m~quisitlos, because such 8L~rlthms ( i~ actumILy implemented } would Irreatly siuptlly the description werk O~ 1:he Lln~uJLst 9 andt at Leant to a cwtaln extent, would ~lna~y ~uL~ilL the strutter eL|eta e promise o~ discovery procedure. aCENOI~L~DG]SX~T I am ~rate~l to Gerald Gazder ~@~ bls w~LuabLe criticisms o~ an ear|lair wersion o~ thlm article. The um]sl di~laisezs app~* REPRRENCES &nalu~Ln, Do 1881= & cotes on the number o~ quorleel needed .to Ldmetl~y refuter L&n~p~a~ta. 1n.~craetl~n 8 Control 51~ 76-87 ~rr~st Ye 1. 19501 & difficulty In the concelpt o~ see*Loll welfare, Journal o£ PoLiticaL Economy 5£t 325 346 ~erwickt R. C. 15~2: Computation sl ~ompL a~ Aty and lexoce I Funct Icnal Gramr, Amelrlcen Journal c~ ComputationaL. LlnEuletLcs ~, ~7-10 c B~oom~lelLd, L. 1926: A set at Kostulales ~ot the eel,nee ot tanguaEe • Lan~vmge 2, 152-1~4 MorBid*l, &. -T. 19S3: Some terse1 resetS, ~J:out Jtratit|cstJcnal 8reszars and their -reLevance to LlnEulmt LOse tho"atlcaL . S~stems theory 16, 2s -s6 Sr emneu~, J. 1983: ~.e mental re presents tLon of Grass at Ice1 relL&t£on8 ((d) MIT Press, Ca~hnidiet Ma See CarroLL, J. Be 1£S2= The study o~ Lma~aGa. Hazard University Press, Cambridao, MaSSe Cheaskyt No 1857: • Syntactic Structures. Mo~tonr~The He6~Ie C~oa~kyt N. 1~56: Three ~dells ~¢r the descrlFtlan ct 1~ el;mlle. ][ .Ee]S • Transactions on [mZormmtioC Theory ~T 2. Cbems~f, 1~0 " 11861= Soma seabed@lesSeeS remrkm on Generative Erammere Word 17, 218-339 C boomK:~e N. 1863: ~arsal ~zcpertJes cf ~M~rs. In: Lucs- Bush- GaLenter (ed~) - Handbook ot eathesatlcel pmycboLo~. 1,Lteyt ~ew ~@rk Cheselt;o H. 1 £7 C : ;omarks on aomim~J~at'lou. In: J~ccba Rosan~aum (eldm)0 Salad IcEs 1~ Esatlsh Trao=f omeLonaL Grammar. Ginn, ~JaLt~m t MIaSmal84 2"~1 Churche- L 1~)80= Cn .~ ;arming strateElee and OL ol~re. Pro~ssdLngs ot the 18th ~Lnou~L ~omtlnE o£ the dCL 107-111 lit,abaca, ~ 1 1974: Automate, lsnaueaes, tad m~chLnms. Academic Press, New Gezder, Ge 1882: Phrase structure iraaeer. In" Jacohsou PuL tUs ( ads ) : ~.he Na.t'~t,o o£ Syntmct'lc Representation. Eol4oLi Dordrecbt 131 1S6 Greenba~m, J R.e Culrk 1970: EtlcltatLon oxpe~Lmont s In • ]~nSL1sh = 11nauiatlc elt~d/~ J.n usalle acd att/t~dae Lon~aa, X-end, s Greene, J. 1872 : Psych.LinGuist ~ ca. Poa~p~Ln o l|~rao~dnor th ;~a~rim, ~ 1946: ]~res acrFhese tc ~tter~n~oo LanMuage, 22~ 1~1-1~3 Harriet • 7.o •.1851: Methods la S~tuctural L2oi~u~mt lose Co,Swarm 11y ot C~ tcalio Prtil Bert/sou, Me. A. 1~78: Introduction t© Pommel , Lan~aje ~.e@ryeAddle@n- temLoyf RmadLnJr Masse Hocker,• C. 1954: ~so aodets 01 8rameatLca~ dosc~lptloo. Vord I C • 210-231 No~kett. Co 195S: A maoua~L of pbane~.©lly. In.ernst lona~ J e~rna~ o~ American Llnaulstlcs• Mmmelz~s 11 Irk.nee• E. 19~1: The c@ocept a~ t In~ul stIc Intuition• In: Canteens (od) : A Peatmchrl~t ~or Native Speaker. Mouton• ~he Haggle, 12~-14C Etnono ~ So Co 1956: 2epreeentat 1an c~ events Ln sar~e nm ti and ~lni qe automata. ~n= Shannon - McCarthy Sods): A~tomata n~d2es. Prises,an University Pre~s 3-41 Lamb. £o M. 1966: Out line 4~ strategies, lama1 arrest. GenrE,taws University Press• ~ashlng.ton DeC. Levi ~tr aunm, C. 1~5~: Ant hropa~c~ie structural.e. Pros• Pm~Ls. L|ebir, ~0 1981: On #he Crganlzatlon ot the Lexicon. IULC Marcus, S. 1S64: Gramme, Sol aI a.utosate flnlte. Edlture AcademieS, Bu~hares~ Marks• L. E. 1968 Scs~ln8 o~ i;r emma, I colneas ot met ~-emJ=edded ~n~llsh sentences. ~orbet Lesrnlnil K Verbal Beh~vler 7• 965 S67 Matthevs• B.J. 1979= Are the gramme, lesT sent,races o~ a len~age s recurslTs sot? Synthese 40, 20~-224 McCullollh • 1. So - lo PLtts 1943: A ~o(~1 ¢aI c8l culum o~ the Ideas Immanent In nervous act Iv i t7. Bulletin o~ m~thmmmtlcal bLophyaiam S, 115-133 McNa~lihton. Re So Paper. _ 1968: She syntactic oooold o~ m + roaster overlie In Arbl~ (ed): Algebraic tboa~y c~ machines• ~.an~agem• and semiEroupmo Academic Proms• l~ow York 297-312 ~cNau~hton • U So Papmrt 1£71: Co~nt sr ~ree automata. ];emesr¢~ Moaotl~ ph no • E 5 t M IT PP ass v GamJ0r Adder Masse nfltlort G. A. - S. fiord 1964: Pree recall em L£ embodded SnGL leh men~ encen• rn~ormotio~ g Central 7, 29~-302 In,rot ~0 P. 1956: Gsdankenoexpsr|aents en ~quont~sL machines. In: Shannon - I/a ~r~hy {oats )= Automata studies. Princeton Only,fairy Press 129 152 l~sweyerw Po J. 1880: ~Juiulstic t~.ecry it~ knor£cae academic Preset New York Fultumt G. and Go Gezdar 19S2: Natural Lan~u&jei and c@stext t Fee LaWd;tlm.~ea. LLngui sties an d PhiLosophy 49 471-~04 P~tname He 1~)61: Soma issues In the ~hecr7 o~ ilra ma r • Proc. Syrup.el • in AppLied Mathematics 19(1 Setcb, PoA. t969: ~he t|nlte~ess ¢t ~ tul~ L lank ~saea* IanGuage 4S, 83 1 843 got:inc, RoJ/* 2959: In dctsnse ot IF. Traoi. Philot. Sea. 11(-144 SnEerer }40 1867: The theory o~ recur~i~Te ~nct Ao~ and etfec~ t~e comput&bLLlty. McGrauoRAll• l~ew ~ork ]fOU re:Ira e We 1875: A grammat Lea1 Ch~actorisetlen Ot sx1:oner, tJal llse LanGuages- Prate 16th S:wmF.oslus cn SeI ,chin41 lq~oo r y and Automat e 13 5-143 S el.omaa~ &o 1973= Paras I Lang~aaee. £cadu£© Press• l~s.~ ~ozk Smll£v~s ~ We Jr. 1~3~0 : Syntax an~ LL-,~p~JJt £c - sam an • 1¢e I n mtratL~£ca*tiome~, theory. In: lirt~- Mo~mlk (rods) Current approaches to eyst8~. AcadeeJc Preset Ne~ Yerk 30 1- 327 ~agvo~ V. He 1~1: ~he depth hYl)othes~n. Zn: J~oh on (ad): Pro(. at Synpesis tn AppLied .Marl:emetics 12• 130-138 7