Commentary on Kaplan and Kay 
Mark Liberman 1 
(University of Pennsylvania) 
Anyone with a fundamental interest in morphology and phonology, either from a 
scientific or a computational perspective, will want to study this long-awaited paper 
carefully. 
Kaplan and Kay (henceforth K&K) announce two goals: "to provide the core of 
a mathematical framework for phonology" and "to establish a solid basis for com- 
putation in the domain of phonological and orthographic systems." They show how 
the algebra of regular relations, with their corresponding automata, can be used to 
compile systems of phonological rules in the style of SPE, including directionality, 
optionality, and ordering. They sketch mechanisms for incorporating a lexicon and 
for dealing with exceptional forms, thus providing a complete treatment in a unified 
framework. 
This accomplishment in itself will not compel the attention of many working pho- 
nologists, who have found good reasons to replace the SPE framework (see Kenstowicz 
\[1994\] for a survey of modern practice), and whose efforts since 1975 have been aimed 
mainly at finding representational primitives to explain typological generalizations, 
support accounts of learning, generalization and change, and provide one end of the 
mapping between symbols and speech. In this effort, there has been little emphasis on 
SPE's goal of giving phonological descriptions an algorithmically specified denotation. 
Perhaps this paper, despite its superficial lack of connection to contemporary work in 
phonology, will set in motion a discussion that will ultimately redress the balance. 
On the computational side, practitioners of practical NLP will be happy to make 
extensive use of the algebra of regular relations, since it provides a truly elegant 
engineering solution to a wide range of problems. However, although direct interpre- 
tation of some simple FSTs can be efficient (e.g. Feigenbaum et al. 1991), and although 
Koskenniemi has documented efficient implementation techniques for his two-level 
systems, the overall architecture presented in this paper is not practically usable as 
written, because of either the size of the resulting automata or the time needed for 
(unwisely implemented) nondeterminism, or both. 
A range of well-known techniques enable programs based on the algebraic com- 
bination of (unary) FSAs to make efficient use of both time and space. Although these 
methods do not apply to FSTs in general, we may presume that K&K have developed 
analogous techniques for the crucial range of cases. With the growing interest in this 
technology, we can expect that either K&K will publish their work or others will reca- 
pitulate it, so that the algebra of regular relations can take its proper and prominent 
place in the toolkit of computational linguistics. 
References 
Feigenbaum, J.; Liberman, M. Y.; and Wright, 
R. N. (1991). "Cryptographic protection of 
databases and software." In Distributed 
Computing and Cryptography, 
edited by J. Feigenbaum and M. Merritt, 
161-172. DIMACS Series, AMS and ACM. 
Kenstowicz, M. (1994). Phonology in 
Generative Grammar. Blackwell. 
1 University of Pennsylvania, 619 Williams Hall, Philadelphia, PA 19104-6305. 
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