A set is a Parikh test set of if is a test set of . We give a characterization of Parikh test sets for arbitrary language in terms of its Parikh basis, and the coincidence graph of letters.
@article{ITA_2008__42_3_525_0, author = {Holub, \v St\v ep\'an}, title = {Parikh test sets for commutative languages}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {42}, year = {2008}, pages = {525-537}, doi = {10.1051/ita:2008011}, mrnumber = {2434033}, zbl = {1149.68068}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2008__42_3_525_0} }
Holub, Štěpán. Parikh test sets for commutative languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) pp. 525-537. doi : 10.1051/ita:2008011. http://gdmltest.u-ga.fr/item/ITA_2008__42_3_525_0/
[1] Polynomial size test sets for commutative languages. RAIRO-Theor. Inf. Appl. 31 (1997) 291-304. | Numdam | MR 1483261 | Zbl 0889.68091
and ,[2] Linear size test sets for certain commutative languages. RAIRO-Theor. Inf. Appl. 35 (2001) 453-475. | Numdam | MR 1908866 | Zbl 1010.68103
and ,[3] Rational cones and commutations. In Machines, languages, and complexity (Smolenice, 1988). Lect. Notes Comput. Sci. 381 (1989) 37-54. | MR 1037563
,