Thomas Jerome Schaefer | |
---|---|
Alma mater | University of California, Berkeley |
Known for | Schaefer's dichotomy theorem |
Scientific career | |
Fields | Computational complexity theory, Game theory |
Institutions | University of California, Berkeley |
Thesis | The Complexity of Some Two-Person Perfect-Information Games (1978) |
Doctoral advisor | Richard M. Karp |
Thomas Jerome Schaefer is an American mathematician.
He obtained his Ph.D. in December 1978 from the University of California, Berkeley, where he worked in the Department of Mathematics. His Ph.D. advisor was Richard M. Karp. [1] [2] [3] [4]
He is well-known for his dichotomy theorem, stating that any problem generalizing Boolean satisfiability in a certain way is either in the complexity class P or is NP-complete. [5]
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable.
Stephen Arthur Cook is an American-Canadian computer scientist and mathematician who has made significant contributions to the fields of complexity theory and proof complexity. He is a university professor emeritus at the University of Toronto, Department of Computer Science and Department of Mathematics.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.
In computer science, the clique problem is the computational problem of finding cliques in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulations of the clique problem include finding a maximum clique, finding a maximum weight clique in a weighted graph, listing all maximal cliques, and solving the decision problem of testing whether a graph contains a clique larger than a given size.
Richard Manning Karp is an American computer scientist and computational theorist at the University of California, Berkeley. He is most notable for his research in the theory of algorithms, for which he received a Turing Award in 1985, The Benjamin Franklin Medal in Computer and Cognitive Science in 2004, and the Kyoto Prize in 2008.
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem.
Martin David Davis was an American mathematician and computer scientist who made significant contributions to the fields of computability theory and mathematical logic. He is best known for his work on Hilbert's tenth problem leading to the MRDP theorem. He also advanced the Post-Turing Model and co-developed the Davis–Putnam–Logemann–Loveland (DPLL) algorithm which is foundational for Boolean satisfiability solvers.
Vijay Virkumar Vazirani is an Indian American distinguished professor of computer science in the Donald Bren School of Information and Computer Sciences at the University of California, Irvine.
Michael Fredric Sipser is an American theoretical computer scientist who has made early contributions to computational complexity theory. He is a professor of applied mathematics and was the Dean of Science at the Massachusetts Institute of Technology.
In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI. Ladner's theorem, shown in 1975 by Richard E. Ladner, is a result asserting that, if P ≠ NP, then NPI is not empty; that is, NP contains problems that are neither in P nor NP-complete. Since it is also true that if NPI problems exist, then P ≠ NP, it follows that P = NP if and only if NPI is empty.
In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem, proved by Thomas Jerome Schaefer, states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables. It is called a dichotomy theorem because the complexity of the problem defined by S is either in P or is NP-complete, as opposed to one of the classes of intermediate complexity that is known to exist by Ladner's theorem.
Umesh Virkumar Vazirani is an Indian–American academic who is the Roger A. Strauch Professor of Electrical Engineering and Computer Science at the University of California, Berkeley, and the director of the Berkeley Quantum Computation Center. His research interests lie primarily in quantum computing. He is also a co-author of a textbook on algorithms.
Richard Jay Lipton is an American computer scientist who is Associate Dean of Research, Professor, and the Frederick G. Storey Chair in Computing in the College of Computing at the Georgia Institute of Technology. He has worked in computer science theory, cryptography, and DNA computing.
Constantinos Daskalakis is a Greek theoretical computer scientist. He is a professor at MIT's Electrical Engineering and Computer Science department and a member of the MIT Computer Science and Artificial Intelligence Laboratory. He was awarded the Rolf Nevanlinna Prize and the Grace Murray Hopper Award in 2018.
Toniann Pitassi is a Canadian-American mathematician and computer scientist specializing in computational complexity theory. She is currently Jeffrey L. and Brenda Bleustein Professor of Engineering at Columbia University and was Bell Research Chair at the University of Toronto.
Oscar H. Ibarra is a Filipino-American theoretical computer scientist, prominent for work in automata theory, formal languages, design and analysis of algorithms and computational complexity theory. He was a Professor of the Department of Computer Science at the University of California-Santa Barbara until his retirement in 2011. Previously, he was on the faculties of UC Berkeley (1967-1969) and the University of Minnesota (1969-1990). He is currently a Distinguished Professor Emeritus at UCSB.
Daniel Mier Gusfield is an American computer scientist, Distinguished Professor of Computer Science at the University of California, Davis. Gusfield is known for his research in combinatorial optimization and computational biology.
In computational complexity, not-all-equal 3-satisfiability (NAE3SAT) is an NP-complete variant of the Boolean satisfiability problem, often used in proofs of NP-completeness.
Alan Louis Selman was a mathematician and theoretical computer scientist known for his research on structural complexity theory, the study of computational complexity in terms of the relation between complexity classes rather than individual algorithmic problems.