Non-systematic Search and Learning: An Empirical Study

This paper explores the performance of a new complete nonsystematic search algorithm learn-SAT on two types of 3-SAT problems, (i) an extended range of AIM problems [1] and (ii) structured unsolvable problems [2]. These are thought to present a difficult challenge for non-systematic search algorithms. They have been extensively used to study powerful special purpose SAT algorithms. We consider two of these, viz. the tableau-based algorithm of Bayardo & Schrag [2] and relsat. We compare their performance with that of learn-SAT, which is based on restart-repair and learning no-goods. Surprisingly, learn-SAT does very well. Sometimes it does much better than the other two algorithms; at other times they are broadly equivalent; and then there are some “anomalies”. One thing at least is clear, learn-SAT solves problems which many would predict are beyond its scope. The relative performance of the three algorithms generates several interesting questions. We point to some of them with a view to future research. The empirical paradigm in this paper reflects some of the views outlined by Mammen & Hogg [10].