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<Paper uid="J80-1001">
  <Title>Cascaded ATN Grammars</Title>
  <Section position="4" start_page="0" end_page="0" type="intro">
    <SectionTitle>
3. Notation
</SectionTitle>
    <Paragraph position="0"> ATN's are characterized as automata by specifying their computations in terms of instantaneous configurations and a transition function that computes possible successor configurations. As such, they can admit a variety of superficial syntaxes, without changing the essential nature of the automaton. In this paper, I will use a notation that is somewhat more concise and slightly more convenient than the original ATN syntax specified in Woods (1970). The major change will be a formal distinction between a phrase type and an initial state for recognizing a phrase. (The original ATN specification used the initial state to serve double duty.) Moreover, I will permit a given phrase type to have several distinct initial states and several phrase types to share some initial states. This permits somewhat greater flexibility in factoring and sharing common parts of different phrase types. The pop arcs of these ATN's will indicate the phrase type being popped, and a given state can be a final state for several phrase types. A BNF specification of the syntax I will use is given, in Figure 1 on the next page.</Paragraph>
    <Paragraph position="1"> A simple example, using the conventions given in the figure, is the following grammar:</Paragraph>
    <Paragraph position="3"> This grammar is equivalent (minus augmentation) to the phrase structure grammar: q--&gt;'a'b, q--&gt;'aq'b.</Paragraph>
    <Paragraph position="4"> It parses a string of n a's followed by nb's and (through its augments) pops the number n.</Paragraph>
  </Section>
class="xml-element"></Paper>