A lower bound for the complexity of Craig's interpolants in sentential logic

  • Daniele Mundici


For any sentenceα (in sentential logic) letdα be the delay complexity of the boolean functionfα represented byα. We prove that for infinitely manyd (and starting with somed<620) there exist valid implicationsα→β withdα,dβd such that any Craig's interpolantx has its delay complexitydχ greater thand+(1/3)·log(d/2). This is the first (non-trivial) known lower bound on the complexity of Craig's interpolants in sentential logic, whose general study may well have an impact on the central problems of computation theory.


Mathematical Logic General Study Central Problem Computation Theory Sentential Logic 
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Copyright information

© Verlag W. Kohlhammer 1983

Authors and Affiliations

  • Daniele Mundici
    • 1
  1. 1.National Research CouncilDonnini (Florence)Italy

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