Constraint satisfaction problems with infinite templates

Abstract. Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a non-uniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ω-categorical. We survey examples of such problems in temporal and spatial reasoning, infinite-dimensional algebra, acyclic colorings in graph theory, artificial intelligence, phylogenetic reconstruction in computational biology, and tree descriptions in computational linguistics. We then give an introduction to the universal-algebraic approach to infinite-domain constraint satisfaction, and discuss how cores, polymorphism clones, and pseudovarieties can be used to study the computational complexity of CSPs with ωcategorical templates. The theoretical results will be illustrated by examples from the mentioned application areas. We close with a series of open problems and promising directions of future research.

Enantioselective intramolecular (2+2)-photocycloaddition reactions of 4-substituted quinolones catalyzed by a chiral sensitizer with a hydrogen-bonding motif

Six 2-quinolones, which bear a terminal alkene linked by a three- or four-membered tether to carbon atom C4 of the quinolone, were synthesized and subjected to an intramolecular [2 + 2]-photocycloaddition. The reaction delivered the respective products in high yields (78-99%) and with good regioselectivity in favor of the straight isomer. If conducted in the presence of a chiral hydrogen-bonding template (2.5 equiv) at low temperature in toluene as the solvent, the reaction proceeded enantioselectively (83-94% ee). An organocatalytic reaction was achieved when employing a chiral hydrogen-bonding template with an attached sensitizing unit (benzophenone or xanthone). The xanthone-based organocatalyst proved to be superior as compared to the respective benzophenone. Closer inspection revealed that the reaction of 4-(pent-4-enyloxy)quinolone leading to a six-membered ring, annelated to the cyclobutane, was less enantioselective (up to 41% ee with 30 mol % catalyst) than the reaction of 4-(but-3-enyloxy)quinolone leading to a five-membered ring (90% ee with 5 mol % and 94% ee with 20 mol % catalyst). Photophysical data (emission spectra, laser flash photolysis experiments) proved that the latter photocycloaddition was significantly faster, supporting the idea that the dissociation of the substrate from the catalyst prior to the photocycloaddition is responsible for the decreased enantioselectivity. Under optimized conditions, employing 10 mol % of the xanthone-based organocatalyst at -25 degrees C in trifluorotoluene as the solvent, three of the other four substrates gave the intramolecular [2 + 2]-photocycloaddition products with high enantioselectivities (72-87% ee). In all catalyzed reactions, the yields based on conversion were moderate to good (40-93%).This work was supported by the Deutsche Forschungsgemeinschaft (DFG) in Germany (Schwerpunktprogramm Organokatalyse and Graduiertenkolleg GRK 1626 Chemical Photocatalyis). Financial support from the Spanish Government is also acknowledged (JAE-doc fellowship for M.C.C. and CTQ2009-13699).Müler, C.; Bauer, A.; Maturi, MM.; Cuquerella Alabort, MC.; Miranda Alonso, MÁ.; Bach, T. (2011). Enantioselective intramolecular (2+2)-photocycloaddition reactions of 4-substituted quinolones catalyzed by a chiral sensitizer with a hydrogen-bonding motif. Journal of the American Chemical Society. 133:16689-16697. doi:10.1021/ja207480qS166891669713