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Title: When Do Homomorphism Counts Help in Query Algorithms?
A query algorithm based on homomorphism counts is a procedure for determining whether a given instance satisfies a property by counting homomorphisms between the given instance and finitely many predetermined instances. In a left query algorithm, we count homomorphisms from the predetermined instances to the given instance, while in a right query algorithm we count homomorphisms from the given instance to the predetermined instances. Homomorphisms are usually counted over the semiring ℕ of non-negative integers; it is also meaningful, however, to count homomorphisms over the Boolean semiring 𝔹, in which case the homomorphism count indicates whether or not a homomorphism exists. We first characterize the properties that admit a left query algorithm over 𝔹 by showing that these are precisely the properties that are both first-order definable and closed under homomorphic equivalence. After this, we turn attention to a comparison between left query algorithms over 𝔹 and left query algorithms over ℕ. In general, there are properties that admit a left query algorithm over ℕ but not over 𝔹. The main result of this paper asserts that if a property is closed under homomorphic equivalence, then that property admits a left query algorithm over 𝔹 if and only if it admits a left query algorithm over ℕ. In other words and rather surprisingly, homomorphism counts over ℕ do not help as regards properties that are closed under homomorphic equivalence. Finally, we characterize the properties that admit both a left query algorithm over 𝔹 and a right query algorithm over 𝔹.  more » « less
Award ID(s):
1814152
PAR ID:
10552698
Author(s) / Creator(s):
; ; ;
Editor(s):
Cormode, Graham; Shekelyan, Michael
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
290
ISSN:
1868-8969
ISBN:
978-3-95977-312-6
Page Range / eLocation ID:
290-290
Subject(s) / Keyword(s):
query algorithms homomorphism homomorphism counts conjunctive query constraint satisfaction Theory of computation → Logic and databases
Format(s):
Medium: X Size: 20 pages; 840787 bytes Other: application/pdf
Size(s):
20 pages 840787 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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