Similarity and bisimilarity notions appropriate for characterizing indistinguishability in fragments of the calculus of relations

Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators such as set difference, projection, coprojection, and residuation. For each considered fragment, a characterization is obtained for when two given binary relational structures are indistinguishable by expressions in that fragment. The characterizations are based on appropriately adapted notions of simulation and bisimulation.Comment: 36 pages, Journal of Logic and Computation 201

Relative Expressive Power of Navigational Querying on Graphs

Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages. We do this not only for general path queries (queries where the result may be any binary relation) but also for boolean or yes/no queries (expressed by the nonemptiness of an expression). For both cases, we present the complete Hasse diagram of relative expressiveness. In particular the Hasse diagram for boolean queries contains some nontrivial separations and a few surprising collapses.Comment: An extended abstract announcing the results of this paper was presented at the 14th International Conference on Database Theory, Uppsala, Sweden, March 201

Bowl Shaped Cavitands Dimerize and Complex Certain Organic Guests in Organic Solvents which Themselves are Poor Guests

The syntheses and binding properties of rigidly bowl-shaped polycyclic cavitands (1—4) are reported. Attached to the four aryl rim positions of the bowls are four benzenes substituted in their para positions with four CC^Me, Br, OH or NO2 groups, which deepen the bowls. Attached to the base of the bowls are four pentyl feet, which increase the solubilities of these hosts in organic solvents. Of the four hosts, only the one containing the CO2Me groups dimerized both in the crystalline state and in solution in ten deute- rated solvents which themselves are poor guests. In three other deuterated solvents, no dimerization was observed. A crystal structure of the dimer showed that one p-MeC^CCs^ group of each monomer occupied the cavity of its complexing partner in a reciprocating double host-guest arrangement. Such a structure is compatible with the ^H-NMR spectra of the dimer in solution. The dimer was also detected in its FAB-MS. The tetrabromocavitand at low concentrations in CD2CI2 complexed MeCC^C^Me, MeCC^Me, PhCC^Me and MeCOC^CC^Me. Tetranitrocavitand 4 also complexed MeC02CH2Me in CD2CI2 as solvent

Repetitions and permutations of columns in the semijoin algebra

Codd defined the relational algebra [E.F. Codd, Communications of the ACM 13 (1970) 377–387; E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed., Prentice-Hall (1972) 65–98] as the algebra with operations projection, join, restriction, union and difference. His projection operator can drop, permute and repeat columns of a relation. This permuting and repeating of columns does not really add expressive power to the relational algebra. Indeed, using the join operation, one can rewrite any relational algebra expression into an equivalent expression where no projection operator permutes or repeats columns. The fragment of the relational algebra known as the semijoin algebra, however, lacks a full join operation. Nevertheless, we show that any semijoin algebra expression can still be simulated in a natural way by a set of expressions where no projection operator permutes or repeats columns