Valiant is world-renowned for his work in
Theoretical Computer Science. Among his many contributions to
Complexity Theory, he introduced the notion of
#P-completeness ("Sharp-P completeness") to explain why enumeration and reliability problems are intractable. He created the
Probably Approximately Correct or PAC model of learning that introduced the field of
Computational Learning Theory and became a theoretical basis for the development of
Machine Learning. He also introduced the concept of
Holographic Algorithms inspired by the
Quantum Computation model. In computer systems, he is most well-known for introducing the
Bulk Synchronous Parallel processing model. Analogous to the von Neumann model for a single computer architecture, BSP has been an influential model for parallel and distributed computing architectures. Recent examples are
Google adopting it for computation at large scale via
MapReduce, MillWheel, Pregel and
Dataflow, and
Facebook creating a graph analytics system capable of processing over 1 trillion edges. There have also been active open-source projects to add explicit BSP programming as well as other high-performance parallel programming models derived from BSP. Popular examples are
Hadoop,
Spark,
Giraph,
Hama,
Beam and
Dask. His earlier work in
Automata Theory includes an
algorithm for context-free parsing, which is still the asymptotically fastest known. He also works in
Computational Neuroscience focusing on understanding memory and learning. Valiant's 2013 book is ''
Probably Approximately Correct: Nature's Algorithms for Learning and Prospering in a Complex World''. In it he argues, among other things, that evolutionary biology does not explain the rate at which evolution occurs, writing, for example, "The evidence for Darwin's general schema for evolution being essentially correct is convincing to the great majority of biologists. This author has been to enough natural history museums to be convinced himself. All this, however, does not mean the current theory of evolution is adequately explanatory. At present the theory of evolution can offer no account of the rate at which evolution progresses to develop complex mechanisms or to maintain them in changing environments." Valiant started teaching at
Harvard University in 1982 and is currently the T. Jefferson Coolidge Professor of Computer Science and Applied Mathematics in the
Harvard School of Engineering and Applied Sciences. Prior to 1982 he taught at
Carnegie Mellon University, the
University of Leeds, and the
University of Edinburgh.
Awards and honors Valiant received the
Nevanlinna Prize in 1986, the
Knuth Prize in 1997, the
EATCS Award in 2008, and the
Turing Award in 2010. He was elected a
Fellow of the Royal Society (FRS) in 1991, and a member of the
United States National Academy of Sciences in 2001. Valiant's nomination for the
Royal Society reads: The citation for his A.M. Turing Award reads: ==Personal life==