10.4230/LIPICS.STACS.2008.1353
Ganzow, Tobias
Tobias
Ganzow
Rubin, Sasha
Sasha
Rubin
Order-Invariant MSO is Stronger than Counting MSO in the Finite
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2008
MSO
Counting MSO
order-invariance
expressiveness
Ehrenfeucht-Fraissé game
Albers, Susanne
Susanne
Albers
Weil, Pascal
Pascal
Weil
2008
2008-02-06
2008-02-06
2008-02-06
en
urn:nbn:de:0030-drops-13535
10.4230/LIPIcs.STACS.2008
978-3-939897-06-4
1868-8969
10.4230/LIPIcs.STACS.2008
LIPIcs, Volume 1, STACS 2008
25th International Symposium on Theoretical Aspects of Computer Science
2013
1
28
313
324
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Albers, Susanne
Susanne
Albers
Weil, Pascal
Pascal
Weil
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2008
1
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
12 pages
186466 bytes
application/pdf
Creative Commons Attribution-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
We compare the expressiveness of two extensions of monadic
second-order logic (MSO) over the class of finite structures. The
first, counting monadic second-order logic (CMSO), extends MSO with
first-order modulo-counting quantifiers, allowing the expression of
queries like ``the number of elements in the structure is even''.
The second extension allows the use of an additional binary
predicate, not contained in the signature of the queried structure,
that must be interpreted as an arbitrary linear order on its
universe, obtaining order-invariant MSO.
While it is straightforward that every CMSO formula can be
translated into an equivalent order-invariant MSO formula, the
converse had not yet been settled. Courcelle showed that for
restricted classes of structures both order-invariant MSO and CMSO
are equally expressive, but conjectured that, in general,
order-invariant MSO is stronger than CMSO.
We affirm this conjecture by presenting a class of structures that
is order-invariantly definable in MSO but not definable in CMSO.
LIPIcs, Vol. 1, 25th International Symposium on Theoretical Aspects of Computer Science, pages 313-324