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<Paper uid="W98-1205">
  <Title>Look-Back and Look-Ahead in the Conversion of Hidden Markov Models into Finite State Transducers</Title>
  <Section position="9" start_page="11" end_page="11" type="concl">
    <SectionTitle>
ANNEX: Regular Expression Operators
</SectionTitle>
    <Paragraph position="0"> Below, a and b designate symbols, A and B designate languages, and R and Q designate relations between two languages. More details on the following operators and pointers to finite-state literature can be found in http://w~, xrce. xerox, com/research/ml~t/f s~  Complement (negation). Set of all strings except those from the language A.</Paragraph>
    <Paragraph position="1"> Term complement. Any symbol other than a.</Paragraph>
    <Paragraph position="2"> Kleene star. Language A zero or more times concatenated with itself.</Paragraph>
    <Paragraph position="3"> A n times. Language A n times concatenated with itself.</Paragraph>
    <Paragraph position="4"> Replace. Relation where every a on the upper side gets mapped to a b on the lower side.</Paragraph>
    <Paragraph position="5">  Symbol pair with a on the upper and b on the lower side.</Paragraph>
    <Paragraph position="6"> Inverse relation where both sides are exchanged with respect to R.</Paragraph>
    <Paragraph position="7"> Concatenation of all strings of A with all strings of B.</Paragraph>
    <Paragraph position="8"> Composition of the relations R and . Empty string (epsilon).</Paragraph>
    <Paragraph position="9"> Any symbol in the known alphabet and its extensions</Paragraph>
  </Section>
class="xml-element"></Paper>