The height of piecewise-testable languages and the complexity of the
logic of subwords
release_zoxpfsdorrahbou735cryrsgyi
by
Prateek Karandikar, Philippe Schnoebelen
2015
Abstract
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
FO^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.
In text/plain
format
Archived Files and Locations
application/pdf 263.6 kB
file_4nrejxy2lbhn3paunt2qpvm5ze
|
arxiv.org (repository) web.archive.org (webarchive) |
1511.01807v1
access all versions, variants, and formats of this works (eg, pre-prints)