The parameterized space complexity of model-checking bounded variable first-order logic

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 15, Issue 3
Main Authors: Chen, Yijia, Elberfeld, Michael, Müller, Moritz
Format: Journal Article Publication
Language:English
Published: Logical Methods in Computer Science e.V 01.01.2019
Subjects:
Algorísmica i teoria de la complexitat
Bounded variable first-order logic
Complexitat computacional
Computational complexity
computer science - logic in computer science
First-order logic
Informàtica
Informàtica teòrica
Llenguatges d'interrogació (Informàtica)
Lògica de primer ordre
Model-checking
Parameterized logarithmic space
Query languages (Computer science)
Àrees temàtiques de la UPC
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary:The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-checking problem for queries with a bounded number of variables. For each bound on the quantifier alternation rank the problem becomes complete for the corresponding level of what we call the tree hierarchy, a hierarchy of parameterized complexity classes defined via space bounded alternating machines between parameterized logarithmic space and fixed-parameter tractable time. We observe that a parameterized logarithmic space model-checker for existential bounded variable queries would allow to improve Savitch's classical simulation of nondeterministic logarithmic space in deterministic space $O(\log^2n)$. Further, we define a highly space efficient model-checker for queries with a bounded number of variables and bounded quantifier alternation rank. We study its optimality under the assumption that Savitch's Theorem is optimal.
ISSN:1860-5974
1860-5974
DOI:10.23638/LMCS-15(3:31)2019