Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
The expressive power of finitely many generalized quantifiers
Information and Computation
Back and forth between guarded and modal logics
ACM Transactions on Computational Logic (TOCL)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
On tractable parameterizations of graph isomorphism
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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We study on which classes of graphs first-order logic (FO) and monadic second-order logic (MSO) have the same expressive power. We show that for each class of graphs that is closed under taking subgraphs, FO and MSO have the same expressive power on the class if, and only if, it has bounded tree depth. Tree depth is a graph invariant that measures the similarity of a graph to a star in a similar way that tree width measures the similarity of a graph to a tree. For classes just closed under taking induced subgraphs, we show an analogous result for guarded second-order logic (GSO), the variant of MSO that not only allows quantification over vertex sets but also over edge sets. A key tool in our proof is a Feferman-Vaught-type theorem that is constructive and still works for unbounded partitions.