A. S. LIBERMAN 
TOWARDS A PHONOLOGICAL ALGORITHM 
The ultimate goal of phonology is to uncover the mechanism 
whereby an indiscrete succession of sounds becomes a discrete chain 
of identifiable phonemes. A word falls naturally into morphemes and 
syllables. In the course of this double division two classes of languages 
emerge: those in which syllable- and morpheme-boundaries always 
coincide and those in which this correspondence is not obligatory. 
In the first case the minimal unit of segmentation is the syllable. In the 
second case we meet with such examples as domus in Latin, reading 
i n English, and so on. Syllabically they are do-mus, rea-ding, morpho- 
logically dora-us, read-ing; the combined scheme is do-m-us, rea-d-ing. 
At the initial stage of processing the sound chain we are only able to 
discriminate between syllabic and phonemic languages, for /In/ in 
domus and/d/in reading are phonemes, i.e. the smallest units of natural 
segmentation in non-syllabic languages. This is the most primitive 
and heuristically the earliest definition of a phoneme that a linguist 
can give. We will formulate the first instructions to the phonologist 
thus: 
(I) Take any bimorphemic word (with a sufftx or ending), di- 
vide it into syllables and by examining the points of morpheme- and 
syllable-division state the presence (resp. absence) of phonemes in the 
languag e . 
.In this paper we shall concern ourselves with phonemic languages. 
The mainspring of further analysis is neutralization and related 
phenomena. Let us take the Russian form \[goT\]. This form is ambi- 
guous and resolves itself into two different roots: god- "year" and 
got- " Goth ". The fact that \[goT\] is the phonetic integument of only 
two forms proves that the distinction between god- and got- lies in one 
segment; if they had two different segments, the form under consi- 
deration would halve resolved itself into at least four roots (n differences 
give 2 -~ or sometimes 2~+ 1 forms): cp. the invented place-name 
\[s'tki\] (\[-\] designates a reduced pretonic vowel), which may equally 
196 ^. s. LIBERMAN 
well represent Sodki, Sadki, Sotki, and Satki and thereby demonstrates 
that sad- and sot- have two points of distinction. Having found out 
that god- and got- constitute a minimal pair, we must localize the dif- 
ference between them. 
The forms of the Genitive case of the two words are g6da and g6ta: 
syllabically go-da, go-ta, morphologically god-a, got-a. We cannot know 
how many phonemes there are in the syllable go-; neither do we know 
whether the case inflexion is monophonemic. But we may be sure 
that the stem-final elements of goda, gota are monophonemic (go-d-a, 
go-t-a as do-m-us, rea-d-ing). We have not learnt to compare phonemes, 
but we can compare go- of go-da, and go- of go-ta. The existence of 
the syllables go-1 and go-z proves that they are able to function as in- 
dependent words: otherwise their separation from the second sylla- 
bles would have been impossible (cp. the English latter - ladder). But 
if they are words (actual or virtual: as a matter of fact ~go/does not 
exist in Russian but/no/,/po\],/to/,/do/, etc. exist), we can test their 
identity. If they prove to be homonyms, the difference between goda 
and gota is concentrated in \]d/- \]t/; if they are non-homonyms, the 
difference lies to the left of/d/- It/, viz. in the vowels.1 Go-1 (from 
go-da) and go-2 (from go-ta) are homonyms, and it follows that/d\] 
and /t/ are indeed different phonemes. The difference between them 
thus stated is the most abstract manifestation of a distinctive feature. 
So far it has nothing to do with phonetics; it is "a something" which 
keeps/d/and/t\[ apart. 
We have detected different phonemes in go-d-a, go-t-a, but we 
do not yet know the status of the stem-final consonant in \[goT\]. A 
chain of simple arguments will convince us that this element is not 
a phoneme of the same rank as /d/or It/. Following the row goda, 
godu, godom, (o) gode (different oblique cases of god-o), we observe 
that the root is everywhere quite unambiguous. Only in the Nomi- 
native case we suddenly acquire a new meaning: \[goT\] is both god-O 
and got-O. A new meaning could not have sprung up, if one and the 
same phoneme went on alternating; consequently, the stem-final pho- 
nemes of goda-godu-godom-gode and god-O cannot be identical. On the 
other hand, the root of gota-gotu-gotom-gote is again unambiguous, 
1 Not in the prevocalic part. for the opposition got- kot ~ he - cat J could not'have 
possibly been neutralized: all events in Russian inflexion happen at the end of the word. 
Also note the importance of the open syllable ingo-da, go-ta: in a dosed syllable we could 
suspect that the difference is covered by the first post-vocalic consonants, 
TOWARDS A PHONOLOGICAL ALGORITHM 197 
and only in got-O we meet with an unexpected new meaning (not 
only got-O but also god-o). So here too the stem-final consonant of 
gota-gotu, etc. is not the same as that ofgot-O. The conclusion is ineluc- 
table that IT\] in \[goT\] does not belong either to/d/or/t/. It is func- 
tionally a very weak element, and whatever its physical properties, it 
is unable to differentiate the morphemes which are distinct in all other 
situations. In \[goT\] both/d/and/t/must have lost the feature which 
otherwise prevents them from merging, and only the non-distinctive 
part must have remained. 
The phenomenon analyzed above is alone worthy to be called 
neutralization. To make sure of it let us esamine the root ro;f-. This 
is also an ambiguous root, for we have rog-O "horn " - ro:~ek "little 
horns" (Gen., P1.) and ro~.-a "mug" (or simply ro~'-O "rye "). A 
comparison of/~/and/g/will give us a distinctive feature just as the 
comparison of/d/and/t/in god-O, got-O. But the ambiguity is present 
in all the cases of the word rosa (ro:~a, ro~i, ro:~e, ro~ei, etc.):/~/does 
not crop up as a result of phonological weakening and is therefore 
a separate phoneme, as /g/. Graphically we may represent the two 
situations in the following way: 
/a/ /t/ 
( a phoneme) (a phoneme) 
 oda 
godu 
godom (o) gode 
/T/ 
(an archiphoneme) 
/g/ 
(a phoneme) (a phoneme) 
gota toga 
gotu rogu 
gotom rogom 
(o) gote (o) roge 
rosa 
ro;~i 
() " 0 l'oze 
ro;~ek 
Our next instructions to the phonologist will be such: 
(II) Examine all the monosyllabic roots of the language. Select 
those which are phonetically ambiguous and can be understood as 
the roots of two different words. Take these words and change them 
into dissyllabics. Find the point of syllable division in both and ascer- 
tain whether the first syllables in them are open. Only words with 
initial open syllables will easily lend themselves to preliminary analysis. 
Compare the left-hand open syllables: if they may be represented as 
different words, the roots under consideration have different vowels; 
198 ^. s. UB~a~A~ 
if the open syllables may be represented as homonyms, the difference 
lies in the postvocalic consonants. The opposition of the contrasting 
phonemes will yield the linguistic basis of the distinctive feature that 
keeps them apart. Study all the possible oppositions and get all the 
distinctive features obtainable by this method. The features will be 
only loosely characterized, e.g. "that which distinguishes the root- 
final consonant of such-and-such words and disappears before a pause " 
The element of the ambiguous form is not an independent phoneme 
if its occurrence is confined to this form. But if some root is ambiguous 
in all its forms and another root only in one form, we have a case of 
two independent phonemes crossing at a single point, so that the pho- 
nological make-up of the constantly ambiguous root remains unchanged. 
When all the distinctive features have been extracted in this way, 
some phonemes will have become uniquely characterized as bundles 
of distinctive features. (It is important that at this stage a phoneme can 
be defined both as a minimal unit of natural segmentation and as a 
bundle of distinctive features, i.e. not only syntagmatically but also 
paradigmatically). But even these phonemes will be tied to the stem- 
final position. We must now learn to recognize these phonemes in 
other contexts, e.g. to identify/d/ in gocla and/d/ in dom "house" 
as one and the same unit. This is the most difficult step, and nothing 
but a tentative solution can be proposed here. It seems that phonemes 
are discovered as purely linguistic entities but identified phonetically. 
After we have obtained the features of the type "that which distinguish- 
es etc. " (see above) we must fred their physical correlates and use 
them as tools of further identification. Human langmage consists of 
sounds, and it could be expected that at some late moment the mate- 
rial implementation of phonemes would come in. 
Our next instructions coristitute a programme, which has already 
taken decades to carry out and whose termination lies in a compara- 
tively distant future. 
(III) Select the phonemes uniquely characterized as bundles of 
distinctive features and find their physical correlates. Use the corre- 
lates as marks whereby to recognize the phonemes in all contexts. 
The Russian phonemes/d t g 2 / and some others are uniquely cha- 
racterized by their distinctive features. But there are phonemes entering 
into few or no alternations. Thus, Ib I and Iv/never alternate in l~us- 
sian,'~and so the specific feature that keeps them apart defies detection. 
To be sure, while studying \[d t g 21 etc., we got a list of distinctive 
TOWARDS A PHONOLOGICAL ALGORITHM 199 
features and later found their correlates. Therefore we can now choose 
some features from the general list and ascribe them to/b/and/v/ 
(e.g./b/will be a stop and/v/a spirant), but the arbitrariness of this 
procedure is apparent. 
Every system of phonemes, if diagrammed, will consist of concen- 
tric circles. The nucleus contains phonemes so active that their beha- 
viour is able to characterize them uniquely. Some phonemes are less 
active (e.g./b/and/v\[ in Russian), others are (almost) non-characte- 
rizable at all (e.g./1 m n r/); in the outermost circle we shall find the 
English/h/and kindred phonemes: these do not enter into any alter- 
nations and cannot be described by distinctive features. Phonemes may 
form a system or a list. Only the nucleus, definable through relevant 
features, deserves the name of system. Peripheral phonemes are juxta- 
posed as letters in an alphabet; they are also kept apart but their cor- 
relates must have an especially wide range of realizations. 
Our next procedure resembles the previous one: 
(IV) Select the phonemes whose characteristics only pardy emerge 
from the alternations and those which are non-definable through their 
linguistic behaviour. Contrary to the nuclear phonemes, these must 
be studied as wholes, both by the linguist and by the instrumentalist. 
A phoneme non-analyzable into distinctive features is itselfa materialized 
feature. 
After we have identified the phonemes in all contexts each of them 
comes out as the invariant of some class of sounds. Hence the final 
definition of a phoneme: it is a minimal unit of natural segmentation 
in non-syllabic languages, a bundle of distinctive features, and the in- 
variant of sounds possessing identical features. 
The implications of the analysis suggested above are too far-rea- 
ching to be discussed here in detail. So only the most important of 
them will be enumerated. 
1) Phonological research presupposes a certain amount of pro- 
sodic, morphological, and semantic data; we cannot start unless we 
know how to divide words into syllables and morphemes and how 
to distinguish homonymous forms and roots from non-homonymous 
ones. 
2) To discover phonemes means to find their syntagmatic 
boundaries and to arrange them into a system. No paradigmatic pro- 
cedures or procedures of identification are possible until the phonemes 
are separated from their neighbours. 
200 A.s. I~IB~RMAIq 
3) Preliminary segmentation and identification concerns stem-final 
consonants. Later they are used as "yardsticks " to define and identify 
stem-initial consonants. Thus, the syntagmatic procedure comes first; 
then follows the paradigmatic identification of phonemes at the end 
of the stem, and only after that the whole string falls into discrete ele- 
ments. Until the last step is made, phonology is divorced from pho- 
netics (except what concerns syllable-division) and is a shadow of 
morphology. 
4) Phonemes form either systems or lists, according as the lan- 
guage is rich or poor in inftexion. 
5) A phonological algorithm starts with the function and ends 
up with realizations. It rejects the idea that phonology is functional 
phonetics and operates on the assumption that phonetics is instrumental 
phonology. 
It is our hope that the procedures discussed in this paper can, in 
principle, serve the basis of an algorithm by which a chain of phonemes 
is generated from an indiscrete sound string. Once this algorithm 
becomes a reality, its programming will be almost a technical problem; 
we shall be able to construct an analogue of the actual speech mecha- 
nism and approach coveted goal, viz. automatic treatment of phonic 
substance. 
