*Alan M. Frisch, Matthew Grum, Chris Jefferson, Bernadette Martínez Hernández, Ian Miguel*

ESSENCE is a new formal language for specifying combinatorial problems in a manner similar to natural rigorous specifications that use a mixture of natural language and discrete mathematics. ESSENCE provides a high level of abstraction, much of which is the consequence of the provision of decision variables whose values can be combinatorial objects, such as tuples, sets, multisets, relations, partitions and functions. ESSENCE also allows these combinatorial objects to be nested to arbitrary depth, thus providing, for example, sets of partitions, sets of sets of partitions, and so forth. Therefore, a problem that requires finding a complex combinatorial object can be directly specified by using a decision variable whose type is precisely that combinatorial object.

*Subjects:* 15.2 Constraint Satisfaction

*Submitted:* Oct 16, 2006

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