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<Paper uid="J86-4003">
  <Title>TECHNICAL CORRESPONDENCE THE EXTRACTION OF A MINIMUM SET OF SEMANTIC PRIMITIVES FROM A MONOLINGUAL DICTIONARY IS NP-COMPLETE</Title>
  <Section position="2" start_page="0" end_page="0" type="evalu">
    <SectionTitle>
DEFINITIONS
</SectionTitle>
    <Paragraph position="0"> 1. A lexicon is a set.</Paragraph>
    <Paragraph position="1"> 2. The elements of a lexicon are called words. 3. A string is a sequence of words.</Paragraph>
    <Paragraph position="2"> 4. The string universe, X*, of a lexicon X is the set of all strings composed of elements of X.</Paragraph>
    <Paragraph position="3"> 5. A language (over a lexicon, X) is a subset of X*. 6. Within a language, L, a definition of a word, w, is some string in L of words within the lexicon (excluding w itself). That is, a definition associates a string with the word being defined.</Paragraph>
    <Paragraph position="4"> 7. A dictonary for a lexicon X is a set of definitions such that each word in X is defined.</Paragraph>
    <Paragraph position="5"> 8. A directed graph G=(N,L) consists of a set N of nodes, together with a set L of ordered pairs of elements of N.</Paragraph>
    <Paragraph position="6"> 9. In a graph G, a directed cycle is a sequence of nodes, (n 1, n 2 ..... n K) in which each of the lines (ni, ni+t) as well as (n K, n 1) is in L.</Paragraph>
  </Section>
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