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Information and Control
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SIAM Journal on Computing
Fixpoint extensions of first-order logic and datalog-like languages
Proceedings of the Fourth Annual Symposium on Logic in computer science
The expressive power of finitely many generalized quantifiers
Information and Computation
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Theoretical Computer Science
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Recognizability Equals Definability for Partial k-Paths
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
First Order Logic, Fixed Point Logic and Linear Order
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Recognizability Equals Monadic Second-Order Definability for Sets of Graphs of Bounded Tree-Width
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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Journal of Combinatorial Theory Series B
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Logspace Versions of the Theorems of Bodlaender and Courcelle
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A logic for PTIME and a parameterized halting problem
Fields of logic and computation
First-Order and Monadic Second-Order Model-Checking on Ordered Structures
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM 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
First-Order and Monadic Second-Order Model-Checking on Ordered Structures
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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It is well-known that least fixed-point logic LFP captures the complexity class PTIME on ordered structures. The ordered conjecture claims that LFP is more expressive than first-order logic FO on every infinite class O of finite ordered structures. We present two methods which yield that LFP is more expressive than FO on various types of classes of ordered structures. The first method, the model-checking method, among others, can be applied for all such classes O of bounded cliquewidth. By the second method, the padding method, we show that for classes O of ``bounded treewidth,'' more precisely, for classes O such that there is a bound for the treewidth of the successor structures associated with the members of O, even DTC is more expressive than FO on O, where DTC denotes the deterministic transitive closure logic, a logic that captures the complexity class L on ordered structures. Furthermore, with the padding method we get that for every infinite class of ordered structures O we have that DTC is more expressive than FO on the class of all ordered sums of pairs of structures in O. Under some complexity theoretic assumption, we prove the existence of a class O of ordered structures such that on O not only LFP is more expressive than FO, but also LFP has the expressive power of existential second-order logic. Furthermore, we characterize those classes of structures whose corresponding class of all ordered versions has bounded treewidth.