Nonconcatenative Finite-State Morphology 
by 
Martin Kay 
Xerox Palo Alto Research Center 
3333 Coyote Hill Road 
Palo Alto. CA 94304. USA 
In the last few years, so called finite.state 
morphology, in general, and two-level 
morphology in particular, have become widely 
accepted as paradigms for the computational 
treatment of morphology. Finite-state 
morphology appeals to the notion of a finite-state 
transducer, which is simply a classical 
finite-state automaton whose transitions are 
labeled with pairs, rather than with single 
symbols. The automaton operates on a pair of 
tapes and advances over a given transition if the 
current symbols on the tapes match the pair on 
the transition. One member of the pair of 
symbols on a transition can be the designated 
null symbol, which we will write ~. When this 
appears, the corresponding tape is not examined, 
and it does not advance as the machine moves to 
the next state. 
Finite-state morphology originally arose out 
of a desire to provide ways of analyzing surface 
forms using grammars expressed in terms of 
systems of ordered rewriting rules. Kaplan and 
Kay (in preparation} observed, that finite-state 
transducers could be used to mimic a large class 
of rewriting rules, possibly including all those 
required for phonology. The importance ,ff this 
came from two considerations. First, transducers 
are indifferent as to the direction in which they 
are applied. In other words, they can be used with 
equal facility to translate between tapes, in either 
direction, to accept or reject pairs of tapes, or to 
generate pairs of tapes. Second, a pair of 
transducers with one tape in common is 
equivalent to a single transducer operating on the 
remaining pair of tapes. A simple algorithm 
exists for constructing the transition diagram fi)r 
this composite machine given those of the origi- 
hal pair. By repeated application of this 
algorithm, it is therefore possible to reduce a 
cascade of transducers, each linked to the next by 
a common tape, to a .~ingie transducer which 
accepts exactly the same pair of tapes as was 
accepted by the original cascade as a whole. From 
these two facts together, it follows that an 
arbitrary ordered set of rewriting rules can be 
modeled by a finite-state transducer which can be 
automatically constructed from them and which 
serves as well for analyzing surface forms as for 
generating them from underlying lexical strings. 
A transducer obtained from an ordered set of 
rules in the way just outlined is a two level device 
in the sense that it mediates directly between 
lexical and surface forms without ever 
constructing the intermediate forms that would 
arise in the course of applying the original rules 
one by one. The term two-level morphology, 
however, is used in a more restricted way, to 
apply to a system in which no intermediate forms 
are posited, even in the original grammatical 
formalism. The writer of a grammar using a 
two-level formalism never needs to think in terms 
of any representations other than the lexical and 
the surface ones. What he does is to specify, using 
one formalism or another, a set of transducers, 
each of which mediates directly between these 
fol'ms and each of which restricts the allowable 
pairs of strings in some way. The pairs that the 
system as a whole accepts are those are those that 
~lre rejected by none of the component 
transducers, modulo certain assumptions about 
the precise way in which they interact, whose 
details need not concern us. Once again, there is 
a formal procedure that can be used to combine 
the set of transducers that make up such a system 
2 
into a single automaton with the same overall 
behavior, so that the final result is 
indistinguishable form that obtained from a set of 
ordered rules. However it is an advantage of 
parallel machines that they can be used with very 
little loss of efficiency without combining them in 
this way. 
While it is not the purpose of this paper to 
explore the formal properties of finite-state 
transducers, a brief excursion may be in order at 
this point to forestall a possible objection to the 
claim that a parallel configuration of transducers 
can be combined into a single one. On the face of 
it, this cannot generally be so because there is 
generally no finite-state transducer that will 
accept the intersection of the sets of tape pairs 
accepted by an arbitrary set of transducers. It is, 
for example, easy to design a transducer that will 
map a string of x's onto the same number of y's 
followed by an arbitrary number of z's. It is 
equally easy to design one that maps a string of 
x's onto the same number of z's preceded by an 
arbitrary number of x's. The intersection of these 
two sets contains just those pairs with some 
number of x's on one tape, and that same number 
of y's followed by the same number of z's on the 
other tape. The set of second tapes therefore 
contains a context-free language which it is 
clearly not within the power of any finite-state 
device to generate. 
Koskenniemi overcame this objection in his 
original work by adopting the view that all the 
transducers in the parallel configuration should 
share the same pair or read-write heads. The 
effect of this is to insist that they not only accept 
the same pairs of tapes, but that they agree on the 
particular sequence of symbol pairs that must be 
rehearsed in the course of accepting each of thetn. 
Kaplan has been able to put a more formal 
construction on this in the following way l,et the 
empty symbols appearing in the pairs labeling 
any transition in the transducers be replaced by 
some ordinary symbol not otherwise part of the 
alphabet. The new set of transducers derived in 
this way clearly do not accept the same pairs of 
tapes as the original ones did, but there is an 
algorithm for constructing a single finite-state 
transducer that will accept the intersection of the 
pairs they all accept. Suppose, now, that this 
configuration of parallel transducers is put in 
series with two other standard transducers, one 
which carries the real empty symbol onto its 
surrogate, and everything else onto itself, and 
another transducer that carries the surrogate 
onto the real empty symbol, then the resulting 
configuration accepts just the desired set of 
languages, all of which are also acceptable by 
single transducers that can be algorithmicalLy 
derived form the originals. 
It may well appear that the systems we have 
been considering properly belong to finite-state 
phonology or graphology, and not to morphology, 
properly construed. Computational linguists 
have indeed often been guilty of some 
carelessness in their use of this terminology. But 
it is not hard to see how it could have arisen. The 
first step in any process that treats natural text is 
to recognize the words it contains, and this 
generally involves analyzing each of them in 
terms of a constituent set of formatives of some 
kind. Most important among the difficulties that 
this entails are those having to do with the 
different shapes that formatives assume in 
different environments. In other words, the 
principal difficulties of morphological analysis 
are in fact phonological or graphological. The 
inventor of two-level morphology, Kimmo 
Koskenniemi, is fact provided a finite-state 
account not just of morphophonemics (or 
morphographemics), but also of morphotactics. 
He took it that the allowable set of words simply 
constituted a regular set of morheme sequences. 
This is probably the more controversial part of his 
proposal, but it is also the less technically 
elaborate, and thereh~re the one that has 
attracted less attention. As a result, the term 
"two-Level morphology" has come to be commonly 
accepted as applying to any system of word 
recognition that involves two-level, finite-state, 
phonology or graphotogy. The approach to 
nonconcatenative morphology to be outlined in 
this paper will provide a more unified treatment 
of morphophonemics and morphotactics than has 
been usual 
3 
I shall attempt to show how a two-level 
account might be given of nonconcatenative 
morphological phenomena, particularly those 
exhibited in the Semitic languages. The 
approach I intend to take is inspired, not only by 
finite-state morphology, broadly construed, but 
equally by autosegmental phonology as proposed 
by Goldsmith (1979) and the autosegmental 
morphology of McCarthy 11979) All the data 
that I have used in this work is taken from 
McCarthy (1979) and my debt to him will be clear 
throughout. 
forms that can be constructed on the basis of each 
of the stems shown. However, there is every 
reason to suppose that, though longer and greatly 
more complex in detail, that enterprise would not 
require essentially different mechanisms from 
the ones I shall describe. 
The overall principles on which the material 
in Table I is organized are clear from a fairly 
cursory inspection. Each form contains the 
letters "ktb" somewhere in it. This is the root of 
the verb meaning "write". By replacing these 
three letters with other appropriately chosen 
Perfective 
Active 
I katab 
II kattab 
III kaatab 
IV ?aktab 
V takattab 
VI takaatab 
VII nkatab 
VIII ktatab 
IX ktabab 
X staktab 
XI ktaabab 
XII ktawtab 
XIII ktawwab 
XIV ktanbab 
XV ktanbay 
Passive 
kutib 
kuttib 
kuutib 
?uktib 
tukuttib 
tukuutib 
nkutib 
ktutib 
stuktib 
Imperfective Participle 
Active Passive Active 
aktub uktab kaatib 
ukattib ukattab mukattib 
ukaatib ukaatab mukaatib 
u?aktib u?aktab mu?aktib 
atakattab utakattab mutkattib 
atakaatab utakaatab mutakaatib 
ankatib unkatab minkatib 
aktatib uktatab muktatib 
aktabib muktabib 
astaktib ustaktab mustaktib 
aktaabib muktaabib 
aktawtib muktawtib 
aktawwib muktawwib 
aktanbib muktanbib 
aktanbiy muktanbiy 
Passive 
maktuub 
mukattab 
mukaatab 
mu?aktab 
mutakattab 
mutakaatab 
munkatab 
muktatab 
mustaktab 
Table 
I take it as my task to describe how the 
members of a paradigm like the one in 'Fable l 
might be generated and recognized effectively 
and efficiently, and in such a way as to capture 
and profit from the principal linguistic 
generalizations inherent in it. Now this is a 
slightly artificial problem because the f,~rms 
given in 'Fable I are not in fact words, but ,rely 
verb stems. To get the verb forms that would be 
found in Arabic text, we should have to expand 
the table very considerably to show the inflected 
I 
sequences of three consonants, we would obtain 
corresponding paradigms for other roots. With 
some notable exceptions, the columns of the table 
contain stems with the same sequence of vowels. 
Each of these is known as a vocalism and, as the 
headings of the columns show, these can serve to 
distinguish perfect from imperfective, active from 
passive, and the like. Each row of the table is 
characterized by a particular pattern according to 
which the vowels and consonants alternate. In 
other words, it is characteristic of a given row 
4 
that the vowel in a particular position is long or 
short, or that a consonant is simple or geminate, 
or that material in one syllable is repeated in the 
following one. McCarthy refers to each of these 
patterns as a prosodic template, a term which I 
shall take over. Each of them adds a particular 
semantic component to the basic verb, making it 
reflexive, causative, or whatever. Our problem, 
will therefore involve designing an abstract 
device capable of combining components of these 
three kinds into a single sequence. Our solution 
will take the form of a set of one or more 
finite-state transducers that will work in parallel 
like those of Koskenniemmi(1983), but on four 
tapes rather than just two. 
There will not be space, in this paper, to give 
a detailed account, even of all the material in 
Table I, not to mention problems that would arise 
if we were to consider the full range of Arabic 
roots. What I do hope to do, however, is to 
establish a theoretical framework within which 
solutions to all of these problems could be 
developed. 
We must presumably expect the transducers 
we construct to account for the Arabic data to 
have transition functions from states and 
quadruples of symbols to states. In other words, 
we will be able to describe them with transition 
diagrams whose edges are labeled with a vector of 
four symbols. When the automaton moves from 
one state to another, each of the four tapes will 
advance over the symbol corresponding to it on 
the transition that sanctions the move. 
I shall allow myself some extensions to this 
basic scheme which will enhance the perspicuity 
and economy of the formalism without changing 
its essential character. In particular, these 
extensions will leave us clearly within the 
domain of finite-state devices. The extensions 
have to do with separating the process of reading 
or writing a symbol on a tape, from advancing the 
tape to the next position. The quadruples that 
label the transitions in the transducers we shall 
be constructing will be elements each consisting 
of two parts, a symbol, and an instruction 
concerning the movement of the tape. l shall use 
the following notation for this. A unadorned 
symbol will be read in the traditional way, 
namely, as requiring the tape on which that 
symbol appears to move to the next position as 
soon as it has been read or written. If the symbol 
is shown in brackets, on the other hand, the tape 
will not advance, and the quadruple specifying 
the next following transition will therefore 
clearly have to be one that specifies the same 
symbol for that tape, since the symbol will still be 
under the read-write head when that transition is 
taken. With this convention, it is natural to 
dispense with the e symbol in favor of the 
notation "\[l", that is, an unspecified symbol over 
which the corresponding tape does not advance. 
A symbol can also be written in braces, in which 
case the corresponding tape will move if the 
symbol under the read-write head is the last one 
on the tape. This is intended to capture the 
notion of spreading, from autosegmental 
morphology, that is, the principal according to 
which the last item in a string may be reused 
when required to fill several positions. 
A particular set of quadruples, or frames, 
made up of symbols, with or without brackets or 
braces, will constitute the alphabet of the 
automata, and the "useful" alphabet must be the 
same for all the automata because none of them 
can move from one state to another unless the 
others make an exactly parallel transition. Not 
surprisingly, a considerable amount of 
information about the language is contained just 
in the constitution of the alphabet. Indeed, a 
single machine with one state which all 
transitions both leave and enter will generate a 
nontrivial subset of the material in Table I. An 
example of the steps involved in generating a 
form that depends only minimally on information 
embodied in a transducer is given in table II. 
The eight step are labeled (a) - (h). For each 
one, a box is shown enclosing the symbols 
currently under the read-write heads. The tapes 
move under the heads from the right and then 
continue to the left. No symbols are shown to the 
right on the bottom tape, because we are 
assuming that the operation chronicled in these 
diagrams is one in which a surface form is 
being 
5 
(a) 
(b) 
(c) 
(d) 
V 
a 
k t 
V C 
a i 
a 
k 
V C 
a 
k 
k t 
V C C 
a 
a k t 
k t b 
C C V 
a 
k t a 
t 
V 
i 
b 
V 
i 
C 
i 
b 
C V 
b 
V C 
C V 
V C 
V C 
V C 
C 
V C 
\[\] 
V 
\[al 
a 
k 
C 
\[\] 
k 
t 
C 
\[\] 
t 
\[\] 
V 
a 
a 
(e) 
(f) 
(g) 
(h) 
V 
a 
V 
a 
V C 
a k 
C C 
k t 
k t b 
V C C V C 
a i 
a k t a b 
k t b 
C C V C V 
a i 
k t a b i 
k t b 
C V C V C 
a i 
t a b i 
k t b 
V C V C 
a i 
a b i b 
V C 
C 
(b} 
C 
\[\] 
b 
\[\] 
V 
i 
i 
b 
C 
\[\] 
b 
Table II 
generated. The bottom tape--the one containing 
the surface form--is therefore being written and 
it is for this reason that nothing appears to the 
right. The other three tapes, in the order shown, 
contain the root, the prosodic template, and the 
vocalism. To the right of the tapes, the frame is 
shown which sanctions the move that will be 
made to advance from that position to the next. 
No such frame is given for the last configuration 
for the obvious reason that this represents the 
end of the process. 
The move from (a) to (b) is sanctioned by a 
frame in which the root consonant is ignored. 
There must be a "V" on the template tape and an 
"a" in the current position of the vocalism. 
However, the vocalism tape will not move when 
the automata move to their next states. Finally, 
there will be an "a" on the tape containing the 
surface form. \[n summary, given that the pros()- 
dic template calls for a vowel, the next vowel in 
the vocalism has been copied to the surface. 
Nondeterministically, the device predicts that 
this same contribution from the vocalism will also 
be required to fill a later position. 
The move from {b) to (c) is sanctioned by a 
frame in which the vocalism is ignored. The 
template requires a consonant and the frame 
accordingly specifies the same consonant on both 
the root and the surface tapes, advancing both of 
them. A parallel move, differing only in the 
identity of the consonant, is made from (c) to (d). 
The move from (d) to (e) is similar to that from (a) 
to (b) except that, this time, the vocalism tape 
does advance. The nondeterministic prediction 
that is being made in this case is that there will 
be no further .~lots for the "a" to fill. Just what it 
is that makes this the "right" move is a matter to 
which we shall return. The move from (e) to (f) 
differs from the previous two moves over root 
consonants in that the "b" is being "spread". In 
other words, the root tape does not move, and this 
possibility is allowed on the specific grounds that 
it is the last symbol on the tape. Once again, the 
automata are making a nondeterministic 
decision, this time that there will be another 
consonant called for later by the prosodic 
template and which it will be possible to fill only 
if this last entry on the root tape does not move 
away. The moves from (f) to (g) and from (g) to Ih) 
are like those from (d) to (e) and (b) to (c) 
respectively. 
Just what is the force of the remark, made 
from time to time in this commentary, that a 
certain move is made nondeterministically? 
These are all situations in which some other move 
was, in fact, open to the transducers but where 
the one displayed was carefully chosen to be the 
one that would lead to the correct result. Suppose 
that, instead of leaving the root tape stationary in 
the move from (e) to (f), it had been allowed to 
advance using a frame parallel to the one used in 
the moves from (b) to (c) and (c) to (d), a frame 
which it is only reasonable to assume must exist 
for all consonants, including "b". The move from 
(f) to (g) could still have been made in the same 
way, but this would have led to a configuration in 
which a consonant was required by the prosodic 
template, but none was available from the root. A 
derivation cannot be allowed to count as complete 
until all tapes are exhausted, so the automata 
would have reached an impasse. We must 
assume that, when this happens, the automata 
are able to return to a preceding situation in 
which an essentially arbitrarily choice was made, 
and try a different alternative. Indeed, we must 
assume that a general backtracking strategy is in 
effect, which ensures that all allowable ~equences 
of choices are explored. 
Now consider the nondeterministic choice 
that was made in the move from {a) to (b), as 
contrasted with the one made under essentially 
indistinguishable circumstances from (d) to le). If 
the vocalism tape had advanced in the first of 
these situations, but not in the second, we should 
presumably have been able to generate the 
putative form "aktibib", which does not exist. 
This can be excluded only if we assume that there 
is a transducer that disallows this sequence of 
events, or if the frames available for "i" are not 
the same as those for "a". We are, in fact, making 
the latter assumption, on the grounds that the 
vowel "i" occurs only in the final position of 
Arabic verb stems. 
Consider, now, the forms in rows II and V of 
table I. In each of these, the middle consonant of 
the root is geminate in the surface. This is not a 
result of spreading as we have described it, 
because spreading only occurs with the last 
consonant of a root. If the prosodic template for 
row II is "CVCCVC", how is that we do not get 
forms like "katbab" and "kutbib" beside the ones 
shown? This is a problem that is overcome in 
McCarthy's autosegmental account only at 
considerable cost. Indeed, is is a deficiency of that 
formalism that the only mechanisms available in 
it to account for gemination are as complex as 
they are, given how common the phenomenon is. 
Within the framework proposed here, 
gemination is provided for in a very natural way. 
Consider the following pair of frame schemata, in 
which c is and arbitrary consonant: 
c \[cl 
C G 
\[I \[1 
c c 
The first of these is the one that was used for the 
consonants in the above example except in the 
situation for the first occurrence of"b", where is 
was being spread into the final two consonantal 
positions of the form. The second frame differs 
from this is two respects. First, the prosodic 
template contains the hitherto unused symbol 
"G". for "geminate", and second, the root tape is 
not advanced. Suppose, now, that the the 
prosodic template for forms like "kattab" is not 
"CVCCVC", but "CVGCVC". It will be possible to 
discharge the "G" only if the root template does 
not advance, so that the following "C" in the 
template can only cause the same consonant to be 
inserted into the word a second time. The 
sequence "GC" in a prosodic template is therefore 
an idiom for consonant gemination. 
Needless to say, McCarthy's work, on which 
this paper is based, is not interesting simply for 
the fact that he is able to achieve an adequate 
description of the data in table I, but also for the 
claims he makes about the way that account 
extends to a wider class of phenomena, thus 
achieving a measure of explanatory power. In 
particular, he claims that it extends to roots with 
two and four consonants. Consider, in particular, 
the following sets of forms: 
ktanbab dhanraj 
kattab dahraj 
takattab tadahraj 
Those in the second column are based on the root 
/dhrj/. In the first column are the corresponding 
forms of /ktb/. The similarity in the sets of 
corresponding forms is unmistakable. They 
exhibit the same patterns of consonants and 
vowels, differing only in that, whereas some 
consonant appears twice in the forms in column 
one, the consonantal slots are all occupied by 
different segments in the forms on the right. For 
these purposes, the "n" of the first pair of forms 
should be ignored since it is contributed by the 
prosodic template, and not by the root. 
consonantal slot in the prosodic template only in 
the case of the shorter form. The structure of the 
second and third forms is equally straighforward, 
but it is less easy to see how our machinery could 
account for them. Once again, the template calls 
for four root consonants and, where only three are 
provided, one must do double duty. But in this 
case, the effect is achieved through gemination 
rather than spreading so that the gemination 
mechanism just outlined is presumably in play. 
That mechanism makes no provision for 
gemination to be invoked only when needed to fill 
slots in the prosodic template that would 
otherwise remain empty. If the mechanism were 
as just described, and the triliteral forms were 
"CVGCVC" and "tVCVGCVC" respectively, then 
the quadriliteral forms would have to be 
generated on a different base. 
It is in cases like this, of which there in fact 
many, that the finite-state transducers play a 
substantive role. What is required in this case is 
a transducer that allows the root tape to remain 
stationary while the template tape moves over a 
"G", provided no spreading will be allowed to 
occur later to fill consonantal slots that would 
not geminate 
spread 
no spread 
l"ig. 1 
Given a triliteral and a quadriliteral root, otherwise be unclaimed. If extra consonants are 
the first pair are exactly as one would expect--the required, then the first priority must be to let 
final root consonant is spread to fill the final them occupy the slots marked with a "G" in the 
template. Fig. 1 shows a schema for the 
transition diagram of a transducer that has this 
effect. I call it a "schema" only because each of 
the edges shown does duty for a number of actual 
transitions. The machine begins in the "start" 
state and continues to return there so long as no 
frame is encountered involving a "G" on the 
template tape. A "G" transition causes a 
nondeterministic choice. If the root tape moves at 
the same time as the "G" is scanned, the 
transducer goes into its "no-spread" state, to 
which it continues to return so long as every move 
over a "C" on the prosodic tape is accompanied by 
a move over a consonant on the root tape. In 
other words, it must be possible to complete the 
process without spreading consonants. The other 
alternative is that the transducer should enter 
the "geminate" state over a transition over a "G" 
in the template with the root tape remaining 
stationary. The transitions at the "geminate" 
state allow both spreading and nonspreading 
transitions. In summary, spreading can occur 
only if the transducer never leaves the "start" 
state and there is no "G" in the template, or there 
is a "G" on the template which does not trigger 
gemination. A "G" can fail to trigger gemination 
only when the root contains enough consonants to 
fill all the requirements that the template makes 
for them. 
One quadriliteral case remains to be 
accounted for, namely the following: 
ktaabab dharjaj 
According to the strategy just elaborated, we 
should have expected the quadriliteral form to 
have been "dhaaraj". But, apparently this form 
contains a slot that is used for vowel lengthening 
with triliteral roots, and as consonantal position 
for quadriliterals. We must therefore presumably 
take it that the prosodic template for this form is 
something like "CCVXCVC" where "X" is a 
segment, but not specified as either w)calic or 
consonantal. This much is in line with the 
proposal that McCarthy himself makes The 
question is, when should be filled by a vowel, and 
when by a consonant? The data in Table I is, of 
course, insufficient to answer question, but a 
plausible answer that strongly suggests itself is 
that the "X" slot prefers a consonantal filler 
except where that would result in gemination. If 
this is true, then it is another case where the 
notion of gemination, though not actually 
exemplified in the form, plays a central role. 
Supposing that the analysis is correct, the next 
question is, how is it to be implemented. The 
most appealing answer would be to make "X" the 
exact obverse of "G", when filled with a 
consonant. In other words, when a root consonant 
fills such a slot, the root tape must advance so 
that the same consonant will no longer be 
available to fill the next position. The possibility 
that the next root consonant would simply be a 
repetition of the current one would be excluded if 
we were to take over from autosegmental 
phonology and morphology, some version of th 
Obligatory Contour Principle (OCP) (Goldsmith, 
1979) which disallows repeated segments except 
in the prosodic template and in the surface string. 
McCarthy points out the roots like/smm/, which 
appear to violate the OCP can invariably be 
reanalyzed as biliteral roots like/sm/and, if this 
is done, our analysis, like his, goes through. 
The OCP does seem likely to cause some 
trouble when we come to treat one of the principal 
remaining problems, namely that of the forms in 
row I of table \[. It turns out that the vowel that 
appears in the second syllable of these forms is 
not provided by the vocalism, but by the root. The 
vowel that appears in the perfect is generally 
different from the one that appears in the 
imperfect, and four different pairs are possible. 
The pair that is used with a given root is an 
idiosyncratic property of that root. One 
possibility is, therefore, that we treat the 
traditional triliterat roots as consisting not 
simply of three consonants, but as three 
consonants with a vowel intervening between the 
second and third, for a total of four segments. 
This flies in the face of traditional wisdom. It also 
runs counter to one of the motivating intuitions of 
autosegmental phonology which would have it 
that particular phonological features can be 
represented on at most one \[exical tier, or tape. 
The intuition is that these tiers or tapes each 
contain a record or a particular kind of 
articulatory gesture; from the hearer's point of 
view, it is as though they contained a record of the 
signal received from a receptor that was attuned 
only to certain features. If we wish to maintain 
this model, there are presumably two 
alternatives open to us. Both involve assuming 
that roots are represented on at least two tapes in 
parallel, with the consonants separate from the 
vowel. 
According to one alternative, the root vowel 
would be written on the same tape as the 
vocalism; according to the other, it would be on a 
tape of its own. Unfortunately, neither 
alternative makes for a particularly happy 
solution. No problem arises from the proposal 
that a given morpheme should, in general, be 
represented on more than one lexical tape. 
However, the idea that the vocalic material 
associated with a root should appear on a special 
tape, reserved for it alone, breaks the clean lines 
of the system as so far presented in two ways. 
First, it spearates material onto two tapes, 
specifically the new one and the vocalism, on 
purely lexical grounds, having nothing to do with 
their phonetic or phonological constitution, and 
this runs counter to the idea of tapes as records of ' 
activity on phonetically specialized receptors. It 
is also at least slightly troublesome in that that 
newly introduced tape fills no function except in 
the generation of the first row of the table. 
Neither of these arguments is conclusive, and 
they could diminish considerably in force as a 
wider range of data was considered. 
Representing the vocalic contribution of the 
root on the same tape as the vacalism would avoid 
both of these objections, but would require that 
vocalic contribution to be recorded either before 
or after the vocalism itself. Since the root vowel 
affects the latter part of the root, it seems 
reasonable that it should be positioned to the 
right. Notice, however, that this is the only 
instance in which we have had to make any 
assumptions about the relative ordering of the 
morphemes that contribute to a stem. Once 
again, it may be possible to assemble further 
evidence reflecting on some such ordering, but l 
do not see it in these data. 
It is only right that I should point out the 
difficulty of accounting satisfactorily for the 
vocalic contribution of verbal roots. It is only 
right that I should also point out that the 
autosegmental solution fares no better on this 
score, resorting, as it must, to rules that access 
essentially non-phonological properties of the 
morphemes involved. By insisting that what I 
have called the spelling of a morpheme should by, 
by definition, be its only contribution to 
phonological processes, ! have cut myself off from 
any such deus ex machina. 
Linguists in general, and computational 
linguists in particular, do well to employ 
finite-state devices wherever possible. They are 
theoretically appealing because they are 
computational weak and best understood from a 
mathematical point of view. They are 
computationally appealing because they make for 
simple, elegant, and highly efficient 
implementaions. In this paper, ! hope I have 
shown how they can be applied to a problem in 
nonconcatenative morphology which seems 
initially to require heavier machinary. 
REFERENCES 
Goldsmith, J A. (1979). Autosegmental 
Phonology. New York; Garland Publishing Inc. 
Kay, M and R. M. Kaplan (in preparation}. 
Phonological Rules and Finite-State Transducers. 
Koskenniemi, K (1983). Two-Level 
Morphology: A General Computational Model \[br 
Word-Form Recognition and Production. 
Doctoral Dissertation, University of Helsinki. 
Leben, W (1973). Suprasegmental 
Phonology. Doctoral Dissertation, MIT, 
Cambridge Massachussetts. 
McCarthy, J J. (1979). Formal problems in 
Semitic Phonology and Morpholog3,. Doctoral 
Dissertation, MIT, Cambridge Massachussetts. 
McCarthy, J J. (1981). "A Prosodic Tehory of 
Nonconcatenative Morphology". Linguistic 
Inquiry, 12.3. 
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