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- Leslie G. Valiant
- Commun. ACM
- 1984

Humans appear to be able to learn new concepts without needing to be programmed explicitly in any conventional sense. In this paper we regard learning as the phenomenon of knowledge acquisition in the absence of explicit programming. We give a precise methodology for studying this phenomenon from a computational viewpoint. It consists of choosing an… (More)

- Leslie G. Valiant
- Commun. ACM
- 1990

The success of the von Neumann model of sequential computation is attributable to the fact that it is an efficient bridge between software and hardware: high-level languages can be efficiently compiled on to this model; yet it can be effeciently implemented in hardware. The author argues that an analogous bridge between software and hardware in required for… (More)

- Leslie G. Valiant
- Theor. Comput. Sci.
- 1979

where the summation is over the n! permutations of (1,2, . . . , n). It is the same as the determinant except that all the terms have positive sign. Despite this similarity, while there are efficient algorithms for computing the determinant all known methods for evaluating the permanent take exponential time. This discrepancy is annoyingly obvious even for… (More)

- Leslie G. Valiant
- SIAM J. Comput.
- 1979

- Leslie G. Valiant, Vijay V. Vazirani
- STOC
- 1985

For all known NP-complete problems the number of solutions in instances having solutions may vary over an exponentially large range. Furthermore, most of the well-known ones, such as satisfiability, are parsimoniously interreducible, and these can have any number of solutions between zero and an exponentially large number. It is natural to ask whether the… (More)

- Leslie G. Valiant, Gordon J. Brebner
- STOC
- 1981

In this paper we isolate a combinatorial problem that, we believe, lies at the heart of this question and provide some encouragingly positive solutions to it. We show that there exists an N-processor <underline>realistic</underline> computer that can simulate arbitrary <underline>idealistic</underline> N-processor parallel computations with only a factor of… (More)

- Michael Kearns, Leslie G. Valiant
- J. ACM
- 1989

In this paper, we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are <italic>representation independent</italic>, in that they hold regardless of the syntactic form in which the learner chooses to… (More)

- Dana Angluin, Leslie G. Valiant
- J. Comput. Syst. Sci.
- 1977

The main purpose of this paper is to give techniques for analysing the probabilistic performance of certain kinds of algorithms, and hence to suggest some fast algorithms with provably desirable probabilistic behaviour. The particular problems we consider are: finding Hamiltonian circuits in directed graphs (DHC), finding Hamiltonian circuits in undirected… (More)

- Leslie G. Valiant
- Handbook of Theoretical Computer Science, Volume…
- 1990

- Leslie G. Valiant
- SIAM J. Comput.
- 1982