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<Paper uid="C88-1043">
  <Title>A Finite State Approach to German Verb Morphology</Title>
  <Section position="4" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 The Finite State Approach
</SectionTitle>
    <Paragraph position="0"> As Gazdar/1985/ \[1\] observed, only very few papers on the mathematical foundations of modern phonology exist. He quotes from Johnson's/1970/PhD thesis \[2\], the earliest study of this kind, who states that &amp;quot;any theory which allows phonological rules to simulate arbitrary rewriting systems is seriously defective, for it asserts next to nothing about the sorts of mappings the rules can perform&amp;quot; (/Johnson 1970\] \[2\], p. 42). According to Gazdar /1985/ (\[1\], p. 2) Johnson &amp;quot;proves that a phonology that permits only simultaneous rule application, as opposed to iterative derivational application, is equivalent to an FST. And he then argues that most of the phonology current around 1970 could eitlmr be formalized or reanalyzed in terms of simultaneous rule application, and could thus be reduced to FSTs.&amp;quot; At the Winter LSA meeting at New York in December 1981, R.</Paragraph>
    <Paragraph position="1"> Kaplan and M. Kay gave a talk -- a written account does nat exist -in which they showed &amp;quot;how the iteratively applied rules of standard generative phonology could, individually, be algorithmically compiled into FSTs&amp;quot; (/Gazdar 1985/\[1\], p. 2) under the constraint that rules may not be reapplied to their own outputs. Such a finite ordered cascade of FSTs can be collapsed into a single FST whose behavior is equivalent to that of the original generative rules (cf./Kay 1983/ \[4\], p. 100-104). A FST is a special kind of finite automaton which operates simultaneously on an input and an output tape such that it inspects two symbols at a time. In Kay's approach, the FSTs carry two labels, each label referring to one of the two tapes. In general, a FST is said to accept a pair of tapes if the symbols on them match a sequence of transitions starting in an initial state and ending in one of the designated final states. If no such sequence can be found, the tapes are rejected. To allow tapes of different length to be accepted, a symbol to be matched against one or other of the tapes to do a transition may be empty, in which case the corresponding tape is ignored.</Paragraph>
    <Paragraph position="2"> There are two advantages with this approach: The first is, that such a combined FST can be implemented easily as a simple and very efficient program. Second, unlike ordered sets of rewriting rules, there is no directionality in principle, so that the same machine can be used for analysis and generation as well.</Paragraph>
    <Paragraph position="3"> Kimmo Koskenniemi /1983a, 1983b, 1984, 1985/\] (\[5\], \[6\], \[7\], \[8\]) took up this approach and applied a variation of it to some heavily inflected languages, first of all to Finnish. His &amp;quot;two-level&amp;quot; model proposes parallel rules instead of successive ones like those of generative phonology. The term &amp;quot;two-level&amp;quot; is supposed to express that there are only two levels, the lexicai and the surface level, and that there are no intermediate ones, even logically. Besides its simplicity -- in particular with respect to implementation -- the problematic ordering of rules is avoided.</Paragraph>
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