Abstract
The aim of this paper is the study of a procedure S given in [11, 13]. We prove that this procedure can compute the closure of the star of a closed recognizable set of words if and only if this closure is also recognizable. This necessary and sufficient condition gives a semi algorithm for the Star Problem. As intermediary results, using S, we give new proofs of some known results.
In the last part, we compare the power of S with the rank notion introduced by Hashigushi [9]. Finally, we characterize the recognizability of the closure of star of recognizable closed sets of words using this rank notion.
This work has been supported by Esprit Basic Research Actions ASMICS II.
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Métivier, Y., Richomme, G., Wacrenier, PA. (1995). Computing the closure of sets of words under partial commutations. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_64
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DOI: https://doi.org/10.1007/3-540-60084-1_64
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