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<Paper uid="P96-1015">
  <Title>Directed Replacement</Title>
  <Section position="10" start_page="114" end_page="114" type="concl">
    <SectionTitle>
7 Appendix: Notational conventions
</SectionTitle>
    <Paragraph position="0"> The regular expression formalism used in this paper is essentially the same as in Kaplan and Kay (1994), in Karttunen (1995), and in Kempe and Karttunen (1996). Upper-case strings, such as UPPER, represent regular languages, and lower-case letters, such as x, represent symbols. We recognize two types of symbols: unary symbols (a, b, c, etc) and symbol pairs (a:x, b:0, etc. ).</Paragraph>
    <Paragraph position="1"> A symbol pair a:x may be thought of as the crossproduct of a and x, the minimal relation consisting of a (the upper symbol) and x (the lower symbol). To make the notation less cumbersome, we systematically ignore the distinction between the language A and the identity relation that maps every string of A into itself. Consequently, we also write a:a as just a.</Paragraph>
    <Paragraph position="2"> Three special symbols are used in regular expressions: 0 (zero) represents the empty string (often denoted by c); ? stands for any symbol in the known alphabet and its extensions; in replacement expressions, .#. marks the start (left context) or the end (right context) of a string. The percent sign, Y,, is used as an escape character. It allows letters that have a special meaning in the calculus to be used as ordinary symbols. Thus Z\[ denotes the literal square bracket as opposed to \[, which has a special meaning as a grouping symbol; %0 is the ordinary zero symbol.</Paragraph>
    <Paragraph position="3"> The following simple expressions appear freqently in the formulas: \[\] the empty string language, ?* the universal (&amp;quot;sigma star&amp;quot;) language.</Paragraph>
    <Paragraph position="4"> The regular expression operators used in the paper are: * zero or more (Kleene star), + one or more (Kleene plus), - not (complement), $ contains, / ignore, I or (union), t~ and (intersection), - minus (relative complement), .x. crossproduct, .o. composition, -&gt; simple replace.</Paragraph>
    <Paragraph position="5"> In the transducer diagrams (Figures 1, 4, etc.), the nonfinal states are represented by single circles, final states by double circles. State 0 is the initial state. The symbol ? represents any symbols that are not explicitly present in the network. Transitions that differ only with respect to the label are collapsed into a single multiply labelled arc.</Paragraph>
  </Section>
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