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<Paper uid="J94-1003">
  <Title>One-Level Phonology: Autosegmental Representations and Rules as Finite Automata</Title>
  <Section position="2" start_page="0" end_page="56" type="abstr">
    <SectionTitle>
1. Introduction
</SectionTitle>
    <Paragraph position="0"> The decade since the publication of Koskenniemi's dissertation (1983) and since the development of the KIMMO system (Karttunen 1983) has witnessed a spectacular flurry of activity as the linguistic and computational consequences of this work have been fleshed out. A considerable body of literature has grown up around TWO-LEVEL MOR-PHOLOGY, along with texts 1 and implementations. 2 The existence of a rule compiler (Koskenniemi 1985) has made it possible for the linguist to work at a conveniently abstract level, and analyses of several languages now exemplify the approach. Today, two-level morphology encompasses much of traditional segmental generative phonology of the SPE variety (Chomsky and Halle 1968). 3 Although further development and application of this model is set to continue for some time, there is now a clear need to integrate it more closely with computational  (Johnson 1972) and there is no guarantee that the transducer encoding an SPE rule can be expressed using the two-level rule notation (Ritchie 1992).</Paragraph>
    <Paragraph position="1"> (~) 1994 Association for Computational Linguistics Computational Linguistics Volume 20, Number 1 grammar frameworks on the one hand and modern nonlinear phonology on the other. The primary goal of this article is to show how the central tenets of autosegmental phonology translate into an implemented finite state model.</Paragraph>
    <Paragraph position="2"> The model is named ONE-LEVEL PHONOLOGY for two reasons. First, the model is monostratal, in that there is only one level of linguistic description. Second, the name is intended to contrast with models employing two levels (such as the FST model mentioned above) or three levels (Goldsmith 1991; Touretzky and Wheeler 1990), or an unbounded number of levels (Chomsky and Halle 1968). The one-level model represents the outgrowth of three independent strands of research: (i) the finite-state modeling of phonology, (ii) the declarative approach to phonology, 4 and (iii) the automatic learning of phonological generalizations (Ellison 1992, 1993).</Paragraph>
    <Paragraph position="3"> The paper is organized as follows. Section 2 presents an overview of autosegmental phonology and the temporal semantics of Bird and Klein (1990). Then we define state-labeled automata (Section 3.1), show their equivalence to finite state automata (Section 3.2), define the operations of concatenation, union, intersection, and complement (Section 3.3), and further define state-labeled transducers (Section 3.4). The central proposals of the paper are contained in Section 4. We show how autosegmental association can be interpreted in terms of the synchronization of two automata, where each automaton specifies an autosegmental tier. We now give a brief foretaste of this procedure. Suppose that we have the autosegmental diagram in (1), encoding high (hi) and round (rnd) autosegments.</Paragraph>
    <Paragraph position="4"> . +hi -hi I/I -rnd +rnd This diagram is encoded as the following expression, where each numeral indicates the number of association lines incident with its corresponding autosegment.</Paragraph>
    <Paragraph position="5"> +hi:l -hi:2 -rnd: 2 +rnd: 1 From this encoding, we can write down the following regular expression. Although such expressions will be opaque at this early stage of the exposition, it suffices to note here that each line of the expression represents a tier and the tiers are combined using the intersection operation (m). Moreover, the ls act as synchronization marks between the operands of the intersection operation.</Paragraph>
    <Paragraph position="6"> (+hi, 0)* (+hi, 1) (+hi, 0)* (-hi, 0)* (-hi, 1)(-hi, 0)* (-hi, 1)(-hi, 0)* m (-rnd, 0)* (-rnd, 1) (-rnd, 0)* (-rnd, 1) (-rnd, 0)* (+rnd, 0)* (+rnd, 1) (+rnd, 0)* The final step is to compute the intersection and project the first element of each tuple (ignoring the ls and 0s). This produces the expression:  Steven Bird and T. Mark Ellison One-Level Phonology Given plausible interpretations of the high and round features, this last expression simplifies to i+a+o +, which describes an automaton tape (or a string) divided into three nonempty intervals, the first containing \[i\], the second containing \[a\], and the third containing \[o\]. This, we shall claim, is the intended interpretation of (1). After a detailed discussion of this procedure, the remainder of Section 4 is given over to generalizing the procedure to an arbitrary number of autosegmental charts (Section 4.4), an evaluation of the encoding with respect to Kornai's desiderata (Section 4.5), and a presentation of the encoding of autosegmental rules (Section 4.6). Finally, Section 5 compares our proposals with those of Kay (1987), Kornai (1991), and Wiebe (1992). While our model has regular grammar power and is fully implemented, these three models go beyond regular grammar power and to our knowledge have never been implemented.</Paragraph>
  </Section>
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