Hyper-optimization for Deterministic Tree Automata

  • Andreas Maletti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7982)

Abstract

A recent minimization technique, called hyper-minimization, permits reductions of language representations beyond the limits imposed by classical semantics-preserving minimization. Naturally, the semantics is not preserved by hyper-minimization; rather the reduced representation, which is called hyper-minimal, can accept a language that has a finite symmetric difference to the language of the original representation. It was demonstrated that hyper-minimization for (bottom-up) deterministic tree automata (dtas), which represent the recognizable tree languages, can be achieved in time \({\cal O}(m \cdot{\log n})\), where m is the size of the dta and n is the number of its states. In this contribution, this result is complemented by two results on the quantity of the errors. It is shown that optimal hyper-minimization for dtas (i.e., computing a hyper-minimal dta that commits the least number of errors of all hyper-minimal dtas) can be achieved in time \({\cal O}(m \cdot n)\). In the same time bound also the number of errors of any hyper-minimal dta can be computed.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andreas Maletti
    • 1
  1. 1.Institute for Natural Language ProcessingUniversität StuttgartStuttgartGermany

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