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<Paper uid="N03-1009">
  <Title>Simpler and More General Minimization for Weighted Finite-State Automata</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> Previous work on minimizing weighted finite-state automata (including transducers) is limited to particular types of weights.</Paragraph>
    <Paragraph position="1"> We present efficient new minimization algorithms that apply much more generally, while being simpler and about as fast.</Paragraph>
    <Paragraph position="2"> We also point out theoretical limits on minimization algorithms. We characterize the kind of &amp;quot;well-behaved&amp;quot; weight semirings where our methods work. Outside these semirings, minimization is not well-defined (in the sense of producing a unique minimal automaton), and even finding the minimum number of states is in general NP-complete and inapproximable.</Paragraph>
  </Section>
class="xml-element"></Paper>