Two Techniques in the Area of the Star Problem

  • Daniel Kirsten
  • Jerzy Marcinkowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1644)

Abstract

Decidability of the Star Problem, the problem whether the language ℙ* is recognizable for a recognizable language ℙ, remains open. We slightly generalize the problem and show that then its decidability status depends strongly on the assumptions considering the trace monoid and finiteness of ℙ. More precisely, we show that for finite set ℙ ⊂ {A, B}* ×{C}* and recognizable ℝ it is decidable whether ℙ* ∩ℝ is recognizable, but the problem becomes undecidable if we consider recognizable (infinite) ℙ or finite ℙ ⊂ {A, B}* × {C, D}*.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Daniel Kirsten
    • 1
  • Jerzy Marcinkowski
    • 2
  1. 1.Department of Computer ScienceDresden University of TechnologyDresdenGermany
  2. 2.Institute of Computer ScienceUniversity of Wroc lawWroc lawPoland

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