Preface to the special issue on Automated Mathematical induction

Two decades ago, Boyer and Moore built one of the first automated theorem provers that are capable of proofs by mathematical induction. Today, the BoyerMoore theorem prover remains the most successful in the field. For a long time, the research on automated mathematical induction was confined to very few people. In recent years, as more people realize the importance of automated inductive reasoning to the use of formal methods of software and hardware development, more automated inductive proof systems have been built. Three years ago, the interested researchers in the field formed two consortia on automated inductive reasoning the MInd consortium in Europe and the IndUS consortium in the United States. The two consortia organized three joint workshops in 1992-1995. There will be another one in 1996. Following the suggestions of Alan Bundy and Deepak Kapur, we edited this special issue to document advances in understanding of the field and in the power of the theorem provers that can be built. The call for papers for the special issue attracted many interesting submissions, and each of them was carefully refereed by the experts in the field. We are very grateful both to those who submitted papers and to the anonymous referees. Six papers were selected for this issue. Unlike other special issues of this journal, we provide the reader with a tutorial study of the Boyer-Moore theorem prover. The other five papers present novel ideas that could be used to build theorem provers more powerful than the Boyer-Moore theorem prover.