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On Some Problems of Mateescu Concerning Subword Occurrences

Ding C., Salomaa A.

Fundamenta Informaticae

2006

Vol. 73, nr 1-2

65-79

The paper investigates inference based on quantities |w|u, the number of occurrences of a word u as a scattered subword of w. Parikh matrices recently introduced are useful tools for such investigations. We introduce and study universal languages for Parikh matrices. We also obtain results concerning the inference from numbers |w|u to w, as well as from certain entries of a Parikh matrix to other entries.

On the Injectivity of Parikh Matrix Mappings

Salomaa A.

Fundamenta Informaticae

2005

Vol. 64, nr 1-4

391-404

We investigate the number of (scattered) subword occurrences and Parikh matrices, especially the case where the matrix determines the word uniquely. A condition introduced in this paper, called g-property, turns out to be a powerful tool for such unambiguous matrices. Interconnections with the general theory of subword histories are also pointed out.