754 research outputs found

    Digital signatures from probabilistically checkable proofs

    Get PDF
    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.Includes bibliographical references (p. 75-77).by Raymond M. Sidney.Ph.D

    Hard Properties with (Very) Short PCPPs and Their Applications

    Get PDF
    We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. Specifically, for every fixed ?, we construct a property P^(?)? {0,1}^n satisfying the following: Any testing algorithm for P^(?) requires ?(n) many queries, and yet P^(?) has a constant query PCPP whose proof size is O(n?log^(?)n), where log^(?) denotes the ? times iterated log function (e.g., log^(2)n = log log n). The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n?polylog(n)). As an immediate application, we obtain stronger separations between the standard testing model and both the tolerant testing model and the erasure-resilient testing model: for every fixed ?, we construct a property that has a constant-query tester, but requires ?(n/log^(?)(n)) queries for every tolerant or erasure-resilient tester

    Interactive Proof Systems

    No full text
    The report is a compilation of lecture notes that were prepared during the course ``Interactive Proof Systems'' given by the authors at Tata Institute of Fundamental Research, Bombay. These notes were also used for a short course ``Interactive Proof Systems'' given by the second author at MPI, Saarbruecken. The objective of the course was to study the recent developments in complexity theory about interactive proof systems, which led to some surprising consequences on nonapproximability of NP hard problems. We start the course with an introduction to complexity theory and covered some classical results related with circuit complexity, randomizations and counting classes, notions which are either part of the definitions of interactive proof systems or are used in proving the above results. We define arthur merlin games and interactive proof systems, which are equivalent formulations of the notion of interactive proofs and show their equivalence to each other and to the complexity class PSPACE. We introduce probabilistically checkable proofs, which are special forms of interactive proofs and show through sequence of intermediate results that the class NP has probabilistically checkable proofs of very special form and very small complexity. Using this we conclude that several NP hard problems are not even weakly approximable in polynomial time unless P = NP

    Some Applications of Coding Theory in Computational Complexity

    Full text link
    Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs

    Probabilistic Proof Systems

    Get PDF
    Various types of probabilistic proof systems have played a central role in the development of computer science in the last decade. In this exposition, we concentrate on three such proof systems -- interactive proofs, zero-knowledge proofs, and probabilistic checkable proofs -- stressing the essential role of randomness in each of them. This exposition is an expanded version of a survey written for the proceedings of the International Congress of Mathematicians (ICM94) held in Zurich in 1994. It is hope that this exposition may be accessible to a broad audience of computer scientists and mathematians
    • …
    corecore