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Quantified Constraints: Algorithms and Complexity
TLDR
This paper considers a more general framework for constraint satisfaction problems which allows arbitrary quantifiers over constrained variables, rather than just existential quantifiers, and shows that the complexity of such extended problems is determined by the surjective polymorphisms of the constraint predicates.
Basics of Galois Connections
  • F. Börner
  • Mathematics
    Complexity of Constraints
  • 23 December 2008
TLDR
Basic properties of Galois connections between sets of relations and sets of functions or generalized functions are given and some tools for the representation of several closure operators on relations as closure operators of some Galois connection are provided.
Maximal partial clones with no finite basis
Abstract. Let A be a nonsingleton finite set. We give a criterion for recognizing not finitely generated strong partial clones and show that none of the |A| strong maximal partial clones of Słupecki
Sets of Permutations and Their Realization by Permutation Networks
In this paper the realization of sets of permutations by permutation networks which are serial connections of some layers with only one binary control input for each layer are systematically
Generating sets for clones and partial clones
TLDR
A criterion for recognizing not finitely generated strong partial clones on a finite set A and applying this criterion to a family of maximal partial clones over A is given.
A note on minimal partial clones
TLDR
It is shown that the atoms of the lattice Lp/sub A/ of all partial clones are either the atomsof Lo/ sub A/ or are generated by partial projections, defined on a totally reflexive and totally symmetric domain.
L O ] 9 S ep 2 00 3 Automorphisms and strongly invariant relations
We investigate characterizations of the Galois connection sInv–Aut between sets of finitary relations on a base set A and their automorphisms. In particular, for A = ω1, we construct a countable set