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We determine the exact power of two-prover interactive proof systems introduced by Ben-Or, Goldwasser, Kilian, and Wigder-son (1988). In this system, two all-powerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input x belongs to the language L. We show that the class of languages having two-prover… (More)

A simple parallel randomized algorithm to find a maximal independent set in a graph G = (V, E) on n vertices is presented. Its expected rmming time on a concurrent-read concurrent-write PRAM with 0(1 E 1 d,,) processors is O(log n), where d,, denotes the maximum degree. On an exclusive-read exclusive-write PRAM with 0(1 El) processors the algorithm runs in… (More)

- László Babai
- STOC
- 1985

In a previous paper [BS] we proved, using the elements of the theory of <italic>nilpotent groups</italic>, that some of the <italic>fundamental computational problems in matriz groups</italic> belong to <italic>NP</italic>. These problems were also shown to belong to <italic>coNP</italic>, assuming an <italic>unproven hypothesis</italic> concerning… (More)

Motivated by Manuel Blum's concept of in-st ante checking, we consider new, very fast and generic mechanisms of checking computations. Our results exploit recent advances in interactive proof protocols [LFKN], [Sh], and especially the MIP = NEXP protocol from [BFL]. WJe show that every nondeterministic computational task S(Z, y), defined as a polynomial… (More)

Let f (xl,. .. . xk) be a Boolean function that k parties wish to collaboratively evaluate, where each xi is a bit-string of length n. The ith party knows each input argument except x,; and each party has unlimited computational power. They share a blackboard, viewed by all parties, where they can exchange messages. The objective is to minimize the number… (More)

We prove the following about the Nearest Lattice Vector Problem (an any e, norm), the Nearest Code-word Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NP-hard. 2. If for some 6 > 0 there exists a polynomial time algorithm that… (More)

We announce an algebraic approach to the problem of assigning <italic>canonical forms</italic> to graphs. We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded valence, in moderately exponential, exp(n<supscrpt>½ + &ogr;(1)</supscrpt>),time for general graphs, in subexponential,… (More)