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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)

We take a complexity theoretic view of A. C. Yao's theory of communication complexity. A rich structure of natural complexity classes is introduced. Besides providing a more structured approach to the complexity of a variety of concrete problems of interest to VLSI, the main objective is to exploit the analogy between Turing machine (TM) and communication… (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)

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)

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)