Name
Abstract | ||
|---|---|---|
We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three logical applications. First, we establish the first known collapse result for the quantifier alternation of MSO logic over countable linear orderings. Second, we solve an open problem posed by Gurevich and Rabinovich, concerning the MSO-definability of sets of rational numbers using the reals in the background. Third, we establish the MSO-definability of the set of yields induced by an MSO-definable set of trees, confirming a conjecture posed by Bruyere, Carton, and Senizergues. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1017/jsl.2018.7 | JOURNAL OF SYMBOLIC LOGIC |
Keywords | Field | DocType |
generalized words,recognizability,monoids,linear orderings,mondaic second-order logic | Discrete mathematics,Rational number,Algebraic number,Countable set,Open problem,Conjecture,Monad (functional programming),Mathematics,Alternation (linguistics) | Journal |
Volume | Issue | ISSN |
83 | 3 | 0022-4812 |
Citations | PageRank | References |
1 | 0.36 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olivier Carton | 1 | 381 | 40.97 |
| Thomas Colcombet | 2 | 327 | 31.61 |
| Gabriele Puppis | 3 | 212 | 20.49 |