Journal ArticleDOI
Pebble Games and Cospectral Graphs
TLDR
This work studies cospectrality from the point of view of pebble games, which are certain type of combinatorial games used in Finite Model Theory to capture the notion of elementary equivalence induced by various logic.About:
This article is published in Electronic Notes in Discrete Mathematics.The article was published on 2017-08-01. It has received 13 citations till now. The article focuses on the topics: Graph isomorphism & Equivalence relation.read more
Citations
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Journal ArticleDOI
On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Properties
TL;DR: Focusing on dimensions k = 1, 2, this work investigates subgraph patterns whose counts are k - WL invariant, and whose occurrence is k -WL invariants, and achieves a complete description of all such patterns for dimension k =1 and considerably extend the previous results known for k = 2.
BookDOI
Language and Automata Theory and Applications, 14th International Conference LATA 2020, Milan, Italy, March 4–6, 2020, Proceedings
TL;DR: This work surveys recent developments related to the Minimum Circuit Size Problem and proposes a strategy to address the problem.
Posted Content
On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Properties
TL;DR: Focusing on dimensions $k=1,2$, this work investigates subgraph patterns whose counts are $k-WL invariant, and whose occurrence is $k$- WL invariants, and achieves a complete description of all such patterns for dimension k=1 and considerably extend the previous results known for k=2.
Book ChapterDOI
On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Properties
TL;DR: The k-dimensional Weisfeiler-Leman algorithm as discussed by the authors is a fruitful approach to the Graph Isomorphism problem and has been shown to be invariant to subgraph patterns for dimension k = 1, 2.
Proceedings ArticleDOI
On the expressive power of homomorphism counts
TL;DR: In this article, a study of the restrictions of the right profile by investigating relaxations of isomorphism that can or cannot be captured by restricting the left profile to a fixed class of graphs is conducted.
References
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Book
Elements of Finite Model Theory
TL;DR: This book describes applications in databases, complexity theory, and formal languages, as well as other branches of computer science, and highlights the computer science aspects of the subject.
Journal ArticleDOI
Which graphs are determined by their spectrum
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: For almost all graphs the answer to the question in the title is still unknown as mentioned in this paper, and the cases for which the answer is known are surveyed in the survey of cases where the Laplacian matrix is known.
Posted Content
Which graphs are determined by their spectrum
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: For almost all graphs the answer to the question in the title is still unknown as mentioned in this paper, and the cases for which the answer is known are surveyed in the survey of cases where the Laplacian matrix is known.
Journal ArticleDOI
Infinitary logics and 0–1 laws
TL;DR: It is shown that the 0–1 law holds for L∞ωω, i.e., the asymptotic probability of every sentence in this logic exists and is equal to either 0 or 1.
Journal ArticleDOI
Logical Hierarchies in PTIME
TL;DR: It is proved that, for each natural numbern, there is a polynomial time computable query which is not definable in any extension of fixpoint logic by any set of generalized quantifiers, which rules out the possibility of characterizing PTIME in terms of definability in fix point logic extended by a finite set of universal quantifiers.