A Sampling-Based Heuristic for Tree Search Applied to Grammar Induction

In the eld of Operation Research and Arti cial Intelligence, several stochastic search algorithms have been designed based on the theory of global random search (Zhigljavsky 1991). Basically, those techniques iteratively sample the search space with respect to a probability distribution which is updated according to the result of previous samples and some prede ned strategy. Genetic Algorithms (GAs) (Goldberg 1989) or Greedy Randomized Adaptive Search Procedures (GRASP) (Feo & Resende 1995) are two particular instances of this paradigm. In this paper, we present SAGE, a search algorithm based on the same fundamental mechanisms as those techniques. However, it addresses a class of problems for which it is di cult to design transformation operators to perform local search because of intrinsic constraints in the de nition of the problem itself. For those problems, a procedural approach is the natural way to construct solutions, resulting in a state space represented as a tree or a DAG. The aim of this paper is to describe the underlying heuristics used by SAGE to address problems belonging to that class. The performance of SAGE is analyzed on the problem of grammar induction and its successful application to problems from the recent Abbadingo DFA learning competition is presented.