Abstract
The satisfaction problem for first-order logic, namely to decide, given a finite structure \(\mathbb{A}\) and a first-order formula φ, whether or not \(\mathbb{A} \models \phi\) is known to be PSpace-complete. In terms of parameterized complexity, where the length of φ is taken as the parameter, the problem is AW[ ⋆ ]-complete and therefore not expected to be fixed-parameter tractable (FPT). Nonetheless, the problem is known to be FPT when we place some structural restrictions on A. For some restrictions, such as when we place a bound on the treewidth of \(\mathbb{A}\), the result is obtained as a corollary of the fact that the satisfaction problem for monadic second-order logic (MSO) is FPT in the presence of such restriction [1]. This fact is proved using automata-based methods. In other cases, such as when we bound the degree of \(\mathbb{A}\), the result is obtained using methods based on the locality of first-order logic (see [3]) and does not extend to MSO. We survey such fixed-parameter tractability results, including the recent [2] and explore the relationship between methods based on automata, locality and decompositions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Courcelle, B.: Graph rewriting: An algebraic and logic approach. In: van Leeuwan, J. (ed.) Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), pp. 193–242. Elsevier, Amsterdam (1990)
Dawar, A., Grohe, M., Kreutzer, S.: Locally excluding a minor. In: Proc. 22nd IEEE Symp. on Logic in Computer Science, IEEE Computer Society Press, Los Alamitos (2007)
Seese, D.: Linear time computable problems and first-order descriptions. Math. Struct. in Comp. Science 6, 505–526 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dawar, A. (2007). Model-Checking First-Order Logic: Automata and Locality. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-74915-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74914-1
Online ISBN: 978-3-540-74915-8
eBook Packages: Computer ScienceComputer Science (R0)