TY  - CONF
A1  - Harwath, Frederik
A1  - Schweikardt, Nicole
A2  - Dürr, Christoph
A2  - Wilke, Thomas
T1  - Regular tree languages, cardinality predicates, and addition-invariant FO
T2  - Christoph Dürr ; Thomas Wilke (Hrsg.): 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012) = Leibniz international proceedings in informatics, 14.2012
N2  - This paper considers the logic FOcard, i.e., first-order logic with cardinality predicates that can specify the size of a structure modulo some number. We study the expressive power of FOcard on the class of languages of ranked, finite, labelled trees with successor relations. Our first main result characterises the class of FOcard-definable tree languages in terms of algebraic closure properties of the tree languages. As it can be effectively checked whether the language of a given tree automaton satisfies these closure properties, we obtain a decidable characterisation of the class of regular tree languages definable in FOcard. Our second main result considers first-order logic with unary relations, successor relations, and two additional designated symbols < and + that must be interpreted as a linear order and its associated addition. Such a formula is called addition-invariant if, for each fixed interpretation of the unary relations and successor relations, its result is independent of the particular interpretation of < and +. We show that the FOcard-definable tree languages are exactly the regular tree languages definable in addition-invariant first-order logic. Our proof techniques involve tools from algebraic automata theory, reasoning with locality arguments, and the use of logical interpretations. We combine and extend methods developed by Benedikt and Segoufin (ACM ToCL, 2009) and Schweikardt and Segoufin (LICS, 2010).
KW  - regular tree languages
KW  - algebraic closure properties
KW  - decidable characterisations
KW  - addition-invariant first-order logic
KW  - logical interpretations
Y1  - 2011
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/23718
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-237188
SN  - 978-3-939897-35-4
SN  - 1868-8969
N1  - © Frederik Harwath and Nicole Schweikardt; licensed under Creative Commons License NC-ND
SP  - 489
EP  - 500
PB  - Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH
CY  - Wadern
ER  -