Algebraic Complexity Theory (Grundlehren der mathematischen Wissenschaften)

Description: Algebraic Complexity Theory (Grundlehren der mathematischen Wissenschaften) [Paperback] B�rgisser, Peter; Clausen, Michael; Shokrollahi, Mohammad A. and Lickteig, T. Product Overview The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems. Read more Details Publisher ‏ : ‎ Springer; Softcover reprint of hardcover 1st ed. 1997 edition (December 5, 2010) Language ‏ : ‎ English Paperback ‏ : ‎ 641 pages ISBN-10 ‏ : ‎ 3642082289 ISBN-13 ‏ : ‎ 83 Item Weight ‏ : ‎ 1.95 pounds Dimensions ‏ : ‎ 6.1 x 1.46 x 9.25 inches Best Sellers Rank: #7,631,076 in Books (See Top 100 in Books) #1,011 in Computer Algorithms #1,035 in Group Theory (Books) #1,232 in Combinatorics (Books) #1,011 in Computer Algorithms #1,035 in Group Theory (Books) We have been selling used books since 2012, and we've learned that the most important thing is doing good business. Honesty is our policy. Free Shipping We ship worldwide. We have multiple warehouses around the world, so please note the extended handling time on certain listings.

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