Compact representation of constraints based on a new interpretation of the concept "tuple of a multi-place relation"

The article discusses various points of view on the concept of "tuple of a multi-place relation" used in mathematics and information technology. Special attention is paid to an evolution of the concept “tuple” within Constraint Programming technology where the emergence of new interpretations for the concept “tuple” is related with attempts to design more “compact” table representation of qualitative relations comparing with typical relational tables. This “compact” representation can serve as a basis for accelerating qualitative constraint satisfaction procedures. In studied prototype-works, such varieties of table constraints as compressed -tables and smart -tables were proposed. In so doing, the concept of compressed - and smart - tuple substantially differs from traditional concept of tuple of a multi-place relation. However, the known table constraints types are not well suited for modeling and processing all types of quality relations, for example, there are inconveniences when modeling production rules. The article proposes a new type of table constraints - smart-tables of D-type and equivalent transformations rules allowing the initial constraint satisfaction problem to be effectively reduced. The application of the smart -tables of D -type allows in some cases to substantially reduce computer memory consumption comparing with application of the known types of table constraints. In particular, smart -tables of D -types are well suited for modeling production rules, some types of logical expirations and some types of global constraints.