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}*.
This work has been supported by the postgraduate program “Specification of discrete processes by operational models and logics” of the German Research Community (Deutsche Forschungsgemeinschaft).
Supported by the Polish KBN grant 8T11C02913.
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Kirsten, D., Marcinkowski, J. (1999). Two Techniques in the Area of the Star Problem. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_45
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DOI: https://doi.org/10.1007/3-540-48523-6_45
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