Unique work on this core topic * Written by internationally recognised specialists in mathematics and computing * Provides the basics for numerous practical industrial applications, e.g. AI, robotics, digital cash
Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The objects of study are algorithms defined within a formal model of computation. Upper bounds on the computational complexity of a problem are usually derived by constructing and analyzing specific algorithms. Meaningful lower bounds on computational complexity are harder to come by, and are not available for most problems of interest. The dominant approach in complexity theory is to consider algorithms as oper ating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot rep resent real or complex numbers, unless the numbers are rounded to approximate values from a discrete set. A major concern of the theory is the number of com putation steps required to solve a problem, as a function of the length of the input string.
Authors and Affiliations
International Computer Science Institute, Berkeley, USA
Lenore Blum
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Lenore Blum,
Felipe Cucker,
Steve Smale
Universitat Pompeu Fabra, Barcelona, Spain
Felipe Cucker
IBM T.J. Watson Research Center, Yorktown Heights, USA
Michael Shub
Bibliographic Information
Book Title: Complexity and Real Computation
Authors: Lenore Blum, Felipe Cucker, Michael Shub, Steve Smale