Cook versus Karp-Levin: Separating Completeness Notions If NP Is Not Small
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Computer Science—the theory, representation, processing, communication and use of information—is fundamentally transforming every aspect of human endeavor. The Department of Computer Science at Iowa State University advances computational and information sciences through; 1. educational and research programs within and beyond the university; 2. active engagement to help define national and international research, and 3. educational agendas, and sustained commitment to graduating leaders for academia, industry and government.
History
The Computer Science Department was officially established in 1969, with Robert Stewart serving as the founding Department Chair. Faculty were composed of joint appointments with Mathematics, Statistics, and Electrical Engineering. In 1969, the building which now houses the Computer Science department, then simply called the Computer Science building, was completed. Later it was named Atanasoff Hall. Throughout the 1980s to present, the department expanded and developed its teaching and research agendas to cover many areas of computing.
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1969-present
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- College of Liberal Arts and Sciences (parent college)
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Abstract
Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is polynomial-time Turing complete (``Cook complete''), but not polynomial-time many-one complete (``Karp-Levin complete''), for NP. This conclusion, widely believed to be true, is not known to follow from P<>NP or other traditional complexity-theoretic hypotheses. Evidence is presented that ``NP does not have p-measure 0'' is a reasonable hypothesis with many credible consequences. Additional such consequences proven here include the separation of many truth-table reducibilities in NP (e.g., k queries versus k+1 queries), the class separation E<>NE, and the existence of NP search problems that are not reducible to the corresponding decision problems.