Two Techniques in the Area of the Star Problem

Authors:
Daniel Kirsten;Jerzy Marcinkowski
Affiliations:
-;-
Venue:
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Year:
1999

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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 IP ⊂ {A,B}* × {C,D}*.