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 
