Two techniques in the area of the star problem in trace monoids

  • Authors:

  • Daniel Kirsten;Jerzy Marcinkowski

  • Affiliations:

  • Institute of Algebra, Dresden University of Technology, D-01062 Dresden, Germany;Institute of Computer Science, University of Wroclaw, ul. Przesmyckiego 20, 51-165 Wroclaw, Poland

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

This paper deals with decision problems related to the star problem in trace monoids which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme (in: I. Privara et al. (Eds.), MFCS'94 Proc., Lecture Notes in Computer Science, vol. 841, Springer, Berlin, 1994, pp. 577-586), we know that the star problem is decidable in trace monoids which do not contain a submonoid of the form {a,c}* × {b,d}*. [cf. Theory Comput. Systems 34(3) (2001) 193-227].Here, we consider a more general problem: Is it decidable whether for some recognizable trace language R and some recognizable or finite trace language P the intersection R ∩ P* is recognizable? If P is recognizable, then we show that this problem is decidable iff the underlying trace monoid does not contain a submonoid of the form {a, c}* × b*. In the case of finite languages P, this problem is decidable in {a,c}* × b* but undecidable in {a,c}* × {b,d}*.