The height of piecewise-testable languages and the complexity of the logic of subwords [article]

Prateek Karandikar, Philippe Schnoebelen
2019 arXiv   pre-print
The height of a piecewise-testable language L is the maximum length of the words needed to define L by excluding and requiring given subwords. The height of L is an important descriptive complexity measure that has not yet been investigated in a systematic way. This article develops a series of new techniques for bounding the height of finite languages and of languages obtained by taking closures by subwords, superwords and related operations. As an application of these results, we show that
more » ... 2(A^*,), the two-variable fragment of the first-order logic of sequences with the subword ordering, can only express piecewise-testable properties and has elementary complexity.
arXiv:1511.01807v4 fatcat:txe7kv7yejchvf3yb2e3ngxysu