Appendix: Conjectures Concerning Proof, Design, and Verification

1 Setting the Stage This article focuses on an esoteric but practical use of automated reasoning that may indeed be new to many, especially those concerned primarily with veriica-tion of both hardware and software. Speciically, featured are a discussion and some methodology for taking an existing design|of a circuit, a chip, a program , or the like|and reening and improving it in various ways. (Although the methodology is general and does not require the use of a speciic program, McCune's program OTTER does ooer what is needed. OTTER has played and continues to play the key role in my research, and an interested person can gain access to this program in various ways, not the least of which is through the included CD-ROM in 3].) When success occurs, the result is a new design that may require fewer components, avoid the use of certain costly components, ooer more reliability and ease of veriication, and, perhaps most important, be more eecient in the contexts of speed and heat generation. Although I have minimal experience in circuit design, circuit validation, program synthesis, program veriication, and similar concerns, (at the encouragement of colleagues based on successes to be cited) I present material that might indeed be of substantial interest to manufacturers and programmers. I write this article in part prompted by the recent activities of chip designers that include Intel and AMD, activities heavily emphasizing the proving of theorems. As for my research that appears to me to be relevant, I have made an intense and most prootable study of nding proofs that are shorter 2,3], some that avoid the use of various types of term, some that are far less complex than previously known, and the like. Those results suggest to me a strong possible connection between more appealing proofs (in mathematics and in logic) and enhanced and improved design of both hardware and software. Here I explore diverse conjectures that elucidate some of the possibly fruitful connections. The strongest argument opposed to what I discuss in this article rests on the great amount of money, time, energy, and expertise that has been devoted to design and related activities. Indeed, one might understandably suspect that such ?