This book principally concerns the rapidly growing area of what might be termed Logical Complexity Theory , the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. Issuing from a two-year NSF and Czech A...cademy of Sciences grant supporting a month-long workshop and 3-day conference in San Diego (1990) and Prague (1991), the book contains refereed articles concerning the existence of the most general unifier, a special case of Kreisel's conjecture on length-of-proof, propositional logic proof size, a new alternating logtime algorithm for boolean formula evaluation and relation to branching programs, interpretability between fragments of arithmetic, feasible interpretability, provability logic, open induction, Herbrand-type theorems, isomorphism between first and second order bounded arithmetics, forcing techniques in bounded arithmetic, ordinal arithmetic in L D o . Also included is an extended abstract of J P Ressayre's new approach concerning the model completeness of the theory of real closed exponential fields. Additional features of the book include (1) the transcription and translation of a recently discovered 1956 letter from K Godel to J von Neumann, asking about a polynomial time algorithm for the proof in k-symbols of predicate calculus formulas (equivalent to the P-NP question), (2) an OPEN PROBLEM LIST consisting of 7 fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references.
Read more