Periodic Reporting for period 3 - CSP-Infinity (Homogeneous Structures, Constraint Satisfaction Problems, and Topological Clones)
Reporting period: 2019-10-01 to 2021-03-31
one concerns for example a powerful extension of the logic MMSNP which has been called MMSNP2, aka guarded disjunctive Datalog: this is still a fragment of existential second-order logic, but now we can also quantify over relations and not just over sets. This logic allows to formulate many more queries that appear in Databases. Again, the goal is to verify the general tractability conjecture for infinite-domain CSPs. Since the general theory of infinite-domain CSPs advances rapidly, this is now within reach.
Another important goal arose from the work of the PI with the PhD Bertalan Bodor (ERC-funded):
it approaches the infinite-domain tractability conjecture by investigating the most symmetric constraint languages first. A mile-stone in this direction would be the verification of the infinite-domain tractability conjecture for all languages that have at most O(c2^(dn)) orbits on injective n-tuples, for all n (and constants c and d). We proved that these are precisely the structures that appear as reducts of finite covers of unary structures, which is a very concrete model-theoretic description that allows us to apply the universal-algebraic approach to constraint satisfaction.