Defining and Using Reformulations

useful in solving tractable problems; for example, the proof of tractability of 2SAT involved the reformulation of 2-SAT as a graph problem (Papadimitriou 1994). However, not enough is known about how and when to apply reformulation. The workshop organizers invited researchers to address the following questions: What is reformulation? How can it be defined formally? Is reformulation different from modeling or search? When and how does one distinguish among them, if at all? What can be gained from reformulation, for example, problem-solving speed, improved understanding of the On 30 October 1998, Mihaela Sabin and I presented the Constraint Problem Reformulation Workshop in conjunction with the Fourth International Conference on the Principles and Practices of Constraint Programming held in Pisa, Italy. Roughly 30 people attended this workshop. This article summarizes the papers presented at the workshop and highlights some of the questions and issues raised during the discussion. The task of selecting the best representation for solving a problem by means of automatically reformulating the problem is a core challenge in AI. Saul Amarel (1968) outlined the impact of different representations of the missionaries and cannibals problem on the performance of the algorithms used to solve the problem. He also proposed automating the reformulation process and, consequently, the process of selecting representations: