Expressiveness of Full First Order Constraints in the Algebra of Finite or Infinite Trees

We are interested in the expressiveness of constraints represented by general first order formulae, with equality as unique relation symbol and function symbols taken from an infinite set F. The chosen domain is the set of trees whose nodes, in possibly infinite number, are labelled by elements of F. The operation linked to each element f of F is the mapping (a1, . . . , an) b, where b is the tree whose initial node is labelled f and whose sequence of daughters is a1, . . . , an. We first consider tree constraints involving long alternated sequences of quantifiers . . .. We show how to express winning positions of two-person games with such constraints and apply our results to two examples. We then construct a family of strongly expressive tree constraints, inspired by a constructive proof of a complexity result by Pawel Mielniczuk. This family involves the huge number (k), obtained by top down evaluating a power tower of 2's, of height k. By a tree constraint of size proportio...

• Type: Conference
• Year: 2000
• Where: CP
• Authors: Alain Colmerauer, Thi-Bich-Hanh Dao
• Keywords: Artificial Intelligence, CP 2000, Expressive Tree Constraints, Infinite Set F, Tree Constraint