The Hot List Strategy

• Authors: Larry Wos;Gail W. Pieper
• Venue: Journal of Automated Reasoning
• Year: 1999

Experimentation strongly suggests that, for attacking deep questions andhard problems with the assistance of an automated reasoning program, themore effective paradigms rely on the retention of deduced information. Asignificant obstacle ordinarily presented by such a paradigm is thededuction and retention of one or more needed conclusions whose complexitysharply delays their consideration. To mitigate the severity of the citedobstacle, I formulated and feature in this article the hot liststrategy. The hot list strategy asks the researcher to choose, usuallyfrom among the input statements characterizing the problem under study, oneor more statements that are conjectured to play a key role for assignmentcompletion. The chosen statements – conjectured to merit revisiting,again and again – are placed in an input list of statements, calledthe hot list. When an automated reasoning program has decided toretain a new conclusion C – before any other statement ischosen to initiate conclusion drawing – the presence of a nonempty hotlist (with an appropriate assignment of the input parameter known asheat) causes each inference rule in use to be applied to Ctogether with the appropriate number of members of the hot list. Members ofthe hot list are used to complete applications of inference rulesand not to initiate applications. The use of the hot list strategythus enables an automated reasoning program to briefly consider a newlyretained conclusion whose complexity would otherwise prevent its use forperhaps many CPU-hours. To give evidence of the value of the strategy, Ifocus on four contexts: (1) dramatically reducing the CPU time required toreach a desired goal, (2) finding a proof of a theorem that had previouslyresisted all but the more inventive automated attempts, (3) discovering aproof that is more elegant than previously known, and (4) answering aquestion that had steadfastly eluded researchers relying on an automatedreasoning program. I also discuss a related strategy, the dynamic hotlist strategy (formulated by my colleague W. McCune), that enables theprogram during a run to augment the contents of the hot list. In theAppendix, I give useful input files and interesting proofs. Because offrequent requests to do so, I include challenge problems to consider,commentary on my approach to experimentation and research, and suggestionsto guide one in the use of McCune’s automated reasoning program OTTER.