Definable isomorphism problem

@article{Keshvardoost2019DefinableIP,
  title={Definable isomorphism problem},
  author={Khadijeh Keshvardoost and Bartek Klin and Slawomir Lasota and Joanna Ochremiak and Szymon Toruńczyk},
  journal={Log. Methods Comput. Sci.},
  year={2019},
  volume={15}
}
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying structure of atoms, we prove decidability of the problem. The core result is parameter-elimination: existence of an isomorphism definable with parameters implies existence of an isomorphism definable without parameters. 

References

SHOWING 1-10 OF 18 REFERENCES
Homomorphism Problems for First-Order Definable Structures
We investigate several variants of the homomorphism problem: given two relational structures, is there a homomorphism from one to the other? The input structures are possibly infinite, but definableExpand
Turing machines with atoms, constraint satisfaction problems, and descriptive complexity
TLDR
Within a substantial class of relational structures including Cai-Fürer-Immerman graphs, those subclasses where the logic IFP+C captures order-invariant polynomial time computation are precisely characterized. Expand
Locally Finite Constraint Satisfaction Problems
TLDR
This work argues that locally finite templates, which contain potentially infinitely many finite relations, occur naturally in Descriptive Complexity Theory, and studies CSPs over such templates for both finite and infinite, definable instances. Expand
Turing Machines with Atoms
TLDR
The main result is that deterministic machines are weaker than nondeterministic ones; in particular, P≠NP in sets with atoms, also known as nominal sets. Expand
A survey of homogeneous structures
TLDR
This article discusses connections between model theory, permutation group theory, combinatorics, and descriptive set theory, and on special properties of an amalgamation class which yield important consequences for the automorphism group. Expand
Automata theory in nominal sets
TLDR
A framework for studying languages over infinite alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet is developed. Expand
SMT Solving for Functional Programming over Infinite Structures
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals withExpand
Graph Isomorphism in Quasipolynomial Time
  • L. Babai
  • Computer Science, Mathematics
  • ArXiv
  • 2015
TLDR
The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques and shows that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioned. Expand
Isomorphism of graphs of bounded valence can be tested in polynomial time
  • E. Luks
  • Computer Science, Mathematics
  • 21st Annual Symposium on Foundations of Computer Science (sfcs 1980)
  • 1980
TLDR
Testing isomorphism of graphs of valence ≤ t is polynomial-time reducible to the color automorphism problem for groups with small simple sections, and some results on primitive permutation groups are used to show that the algorithm runs inPolynomial time. Expand
Reachability Analysis of First-order Definable Pushdown Systems
TLDR
The reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures and the technique is able to give concrete complexity upper bounds for the more restrictive homogeneous structures. Expand
...
1
2
...