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Expressive Power of Tree Logics

Objective

Logics for expressing properties of labeled trees and forests figure importantly in several different areas of Computer Science, including verification (branching temporal logics) and database theory (many XML query languages). The goal of this project is to investigate the expressive power of tree logics, mainly those logics that can be captured by tree automata. A similar study, but for word languages, is one of the main lines of research in formal language theory. The study of the expressive power of word logics has lead to many beautiful and fundamental results, including Schutzenberger's characterization of star-free languages, and the Krohn-Rhodes decomposition theorem. We intend to extend this research for trees. The type of questions we want to answer is: what is the expressive power of first-order logic in trees? is there a Krohn-Rhodes decomposition theory for trees? what is a tree group? We expect that our study of tree logics will use algebraic techniques, possibly the setting of forest algebra (as introduced by the principal investigator and Igor Walukiewicz). We would also like to extend the algebraic setting beyond regular languages of finite trees, to e.g. infinite trees, or nonregular languages.

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /humanities/languages and literature/languages - general
  • /natural sciences/biological sciences/botany

Call for proposal

ERC-2009-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

UNIWERSYTET WARSZAWSKI
Address
Krakowskie Przedmiescie 26/28
00 927 Warszawa
Poland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 799 920
Principal investigator
Mikolaj Bojanczyk (Mr.)
Administrative Contact
Mikolaj Bojanczyk (Dr.)

Beneficiaries (1)

UNIWERSYTET WARSZAWSKI
Poland
EU contribution
€ 799 920
Address
Krakowskie Przedmiescie 26/28
00 927 Warszawa
Activity type
Higher or Secondary Education Establishments
Principal investigator
Mikolaj Bojanczyk (Mr.)
Administrative Contact
Mikolaj Bojanczyk (Dr.)