Algorithmic Solutions via Model Theoretic Interpretations

@inproceedings{Zaid2017AlgorithmicSV,
  title={Algorithmic Solutions via Model Theoretic Interpretations},
  author={F. A. Zaid and D. Kuske and E. Gr{\"a}del},
  year={2017}
}
Model theoretic interpretations are an important tool in algorithmic model theory. Their applications range from reductions between logical theories to the construction of algorithms for problems, which are hard in general but efficiently solvable on restricted classes of structures, like 3-Colorability on graphs of bounded treewidth. We investigate this tool in three different areas of Algorithmic Model Theory: 1. automata-based decision procedures for logical theories, 2. algorithmic meta… Expand
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References

SHOWING 1-10 OF 111 REFERENCES
Automatic structures
  • Achim Blumensath, E. Grädel
  • Computer Science
  • Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
TLDR
This work determines the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic and gives model-theoretic characterisations for automatic structures via interpretations. Expand
Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree
TLDR
This work proposes a general method based on Ehrenfeucht-Fraisse games to give upper bounds on the size of these automata and on the time required to build them and concludes that the very general and simple automata-based algorithm works well to decide the first-order theories over these structures. Expand
Decidability of second-order theories and automata on infinite trees
Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involvesExpand
Ehrenfeucht-Fraïssé goes automatic for real addition
  • F. Klaedtke
  • Computer Science, Mathematics
  • Inf. Comput.
  • 2010
TLDR
A double exponential upper bound on the automata size for FO(R,+,<) and an exponential upper bounds for the first-order theory of the discrete order over the integers FO(Z,<) are established. Expand
Feasible computation through model theory
The computational complexity of a problem is usually defined in terms of the resources required on some machine model of computation. An alternative view looks at the complexity of describing theExpand
Upper Bounds on the Automata Size for Integer and Mixed Real and Integer Linear Arithmetic (Extended Abstract)
TLDR
This work defines two graded back-and-forth systems, and uses them to derive bounds on the automata size by establishing a connection between those systems and languages that can be described by formulas in the respective logics. Expand
Complete Problems for Fixed-Point Logics
TLDR
This class gives a natural description of the fixed-point process of an inductive fix-point formula and hence sheds some light on completely different aspects of the logic than Dahlhaus's construction, which is strongly based on the features of least fixed- point formulae. Expand
Logic, graphs, and algorithms
  • Martin Grohe
  • Computer Science, Mathematics
  • Logic and Automata
  • 2007
TLDR
An introduction into the theory underlying algorithmic meta theorems and a survey of the most important results in this area are presented. Expand
A hierarchy of tree-automatic structures
TLDR
It is obtained that there exist infinitely many ωn- automatic, hence also ω-tree-automatic, atomless boolean algebras, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorph under an alternate axiom AT, strengthening a result of [14]. Expand
A Hierarchy of Automatic Words having a Decidable MSO Theory
We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectivelyExpand
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