{"title":"Peter Clote","description":null,"products":[{"product_id":"boolean-functions-and-computation-models-book-peter-clote-9783540594369","title":"Boolean Functions and Computation Models","description":"The foundations of computational complexity theory go back to Alan Thring in the 1930s who was concerned with the existence of automatic procedures deciding the validity of mathematical statements. The first example of such a problem was the undecidability of the Halting Problem which is essentially the question of debugging a computer program: Will a given program eventu­ ally halt? Computational complexity today addresses the quantitative aspects of the solutions obtained: Is the problem to be solved tractable? But how does one measure the intractability of computation? Several ideas were proposed: A. Cobham [Cob65] raised the question of what is the right model in order to measure a \"computation step\" , M. Rabin [Rab60] proposed the introduction of axioms that a complexity measure should satisfy, and C. Shannon [Sha49] suggested the boolean circuit that computes a boolean function. However, an important question remains: What is the nature of computa­ tion? In 1957, John von Neumann [vN58] wrote in his notes for the Silliman Lectures concerning the nature of computation and the human brain that . . . logics and statistics should be primarily, although not exclusively, viewed as the basic tools of 'information theory'. Also, that body of experience which has grown up around the planning, evaluating, and coding of complicated logical and mathematical automata will be the focus of much of this information theory. The most typical, but not the only, such automata are, of course, the large electronic computing machines.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49575526629649,"sku":"GOR013749986","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52482989687057,"sku":"NLS9783540594369","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540594361.jpg?v=1751253032"},{"product_id":"computational-molecular-biology-book-rolf-backofen-9780471872511","title":"Computational Molecular Biology","description":"This introductory level text is suitable for use by advanced undergraduate and graduate students of computational biology. Written by experienced authors, it provides detailed coverage of many algorithms, including applications and possible modifications.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51137314652433,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51137318813969,"sku":"NIN9780471872511","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52336198942993,"sku":"NLS9780471872511","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0471872512.jpg?v=1764239254"},{"product_id":"arithmetic-proof-theory-and-computational-complexity-book-peter-clote-9780198536901","title":"Arithmetic, Proof Theory, and Computational Complexity","description":"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 Academy 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 Λ Δ  o . Also included is an extended abstract of J P Ressayre's new approach concerning the model completeness of the theory of real closed expotential 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.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51179319787793,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51179321852177,"sku":"NIN9780198536901","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52403090325777,"sku":"NLS9780198536901","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0198536909.jpg?v=1751100999"},{"product_id":"boolean-functions-and-computation-models-book-peter-clote-9783642082177","title":"Boolean Functions and Computation Models","description":"The foundations of computational complexity theory go back to Alan Thring in the 1930s who was concerned with the existence of automatic procedures deciding the validity of mathematical statements. The first example of such a problem was the undecidability of the Halting Problem which is essentially the question of debugging a computer program: Will a given program eventu­ ally halt? Computational complexity today addresses the quantitative aspects of the solutions obtained: Is the problem to be solved tractable? But how does one measure the intractability of computation? Several ideas were proposed: A. Cobham [Cob65] raised the question of what is the right model in order to measure a \"computation step\" , M. Rabin [Rab60] proposed the introduction of axioms that a complexity measure should satisfy, and C. Shannon [Sha49] suggested the boolean circuit that computes a boolean function. However, an important question remains: What is the nature of computa­ tion? In 1957, John von Neumann [vN58] wrote in his notes for the Silliman Lectures concerning the nature of computation and the human brain that . . . logics and statistics should be primarily, although not exclusively, viewed as the basic tools of 'information theory'. Also, that body of experience which has grown up around the planning, evaluating, and coding of complicated logical and mathematical automata will be the focus of much of this information theory. The most typical, but not the only, such automata are, of course, the large electronic computing machines.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52481637024017,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481637941521,"sku":"NLS9783642082177","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642082177.jpg?v=1759852018"},{"product_id":"feasible-mathematics-ii-book-peter-clote-9781461275824","title":"Feasible Mathematics II","description":"Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa­ tion device, such as a 'lUring machine or boolean circuit. Feasible math­ ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa­ rameters of the problem are the cause of its computational complexity and completeness, density and separation\/collapse results are given for a struc­ ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52617595945233,"sku":"NLS9781461275824","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461275824.jpg?v=1761530775"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-peter-clote.oembed","provider":"World of Books ","version":"1.0","type":"link"}