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Manuel Blum 0001

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

16 papers
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16

FOCS Conference 1994 Conference Paper

Program Result-Checking: A Theory of Testing Meets a Test of Theory

  • Manuel Blum 0001
  • Hal Wasserman

We review the field of result-checking, discussing simple checkers and self-correctors. We argue that such checkers could profitably be incorporated in software as an aid to efficient debugging and reliable functionality. We consider how to modify traditional checking methodologies to make them more appropriate for use in real-time, real-number computer systems. In particular, we suggest that checkers should be allowed to use stored randomness: i. e. , that they should be allowed to generate, pre-process, and store random bits prior to run-time, and then to use this information repeatedly in a series of run-time checks. In a case study of checking a general real-number linear transformation (for example, a Fourier Transform), we present a simple checker which uses stored randomness, and a self-corrector which is particularly efficient if stored randomness is allowed. >

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FOCS Conference 1992 Conference Paper

Towards a Computational Theory of Statistical Tests (Extended Abstract)

  • Manuel Blum 0001
  • Oded Goldreich 0001

The authors initiate a computational theory of statistical tests. Loosely speaking, an algorithm is a statistical test if it rejects a 'negligible' fraction of strings. A statistical test is universal for a class of algorithms if it rejects all (but finitely many) of the strings rejected by each algorithm in the class. They consider the existence and efficiency of universal statistical tests for various classes of statistical tests. They also consider the relation between ensembles passing statistical tests of particular complexity and ensembles which are indistinguishable from uniform by algorithms of the same complexity. Some results refer to relatively simple statistical tests (e. g. those implemented by counter machines). >

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FOCS Conference 1991 Conference Paper

Checking the Correctness of Memories

  • Manuel Blum 0001
  • William S. Evans
  • Peter Gemmell
  • Sampath Kannan
  • Moni Naor

The notion of program checking is extended to include programs that alter their environment, in particular, programs that store and retrieve data from memory. The model considered allows the checker a small amount of reliable memory. The checker is presented with a sequence of requests (online) to a data structure which must reside in a large but unreliable memory. The data structure is viewed as being controlled by an adversary. The checker is to perform each operation in the input sequence using its reliable memory and the unreliable data structure so that any error in the operation of the structure will be detected by the checker with high probability. Checkers for various data structures are presented. Lower bounds of log n on the amount of reliable memory needed by these checkers, where n is the size of the structure, are proved. >

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FOCS Conference 1987 Conference Paper

Generic Oracles and Oracle Classes (Extended Abstract)

  • Manuel Blum 0001
  • Russell Impagliazzo

In this paper, we examine various complexity issues relative to an oracle for a generic set in order to determine which are the more "natural" conjectures for these issues. Generic oracle results should be viewed as parallels to random oracle results, as in [BG]; the two are in many ways related, but, as we shall exhibit, not equivalent. Looking at computation relative to a generic oracle is in some ways a better reflection of computation without an oracle; for example, whereas adding a random oracle allows a deterministic polynomial-time machine to solve any problem in BPP, adding a generic oracle will not help solve any recursive problem faster than it could be solved without an oracle. Generic sets were first introduced by Cohen as a tool for proving independence results in set theory [Co]. Their recursion theoretic properties have also been explored in depth; for example, see [J] and [Ku2]. Some related work using forcing and/or generic sets as tools in oracle constructions can be found in [Ku3], [Do], [P], and [A-SFH]. However, this is to our knowledge the first knowledge the first thorough examination of complexity relative to a generic Oracle.

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FOCS Conference 1984 Conference Paper

Independent Unbiased Coin Flips From a Correlated Biased Source: a Finite State Markov Chain

  • Manuel Blum 0001

von Neumann's trick for generating an absolutely unbiased coin from a biased one is this: 1. Toss the biased coin twice, getting 00, 01, 10, or 11. 2. If 00 or 11 occur, go back to step 1; else 3. Call 10 a H, 01 a T. Since p[H] = p[1]*p[0] = p[T], the output is unbiased. Example: 00 10 11 01 01 /spl I. oarr/ H T T. Peter Elias gives an algorithm to generate an independent unbiased sequence of Hs and Ts that nearly achieves the Entropy of the one-coin source. His algorithm is excellent, but certain difficulties arise in trying to use it (or the original von Neumann scheme) to generate bits in expected linear time from a Markov chain. In this paper, we return to the original one-coin von Neumann scheme, and show how to extend it to generate an independent unbiased sequence of Hs and Ts from any Markov chain in expected linear time. We give a right and wrong way to do this. Two algorithms A and B use the simple von Neumann trick on every state of the Markov chain. They differ in the time they choose to announce the coin flip. This timing is crucial.

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STOC Conference 1972 Conference Paper

Linear Time Bounds for Median Computations

  • Manuel Blum 0001
  • Robert Floyd 0001
  • Vaughan R. Pratt
  • Ronald L. Rivest
  • Robert Endre Tarjan

New upper and lower bounds are presented for the maximum number of comparisons, f(i,n), required to select the i-th largest of n numbers. An upper bound is found, by an analysis of a new selection algorithm, to be a linear function of n: f(i,n) ≤ 103n/18 < 5.73n, for 1 ≤ i ≤ n. A lower bound is shown deductively to be: f(i,n) ≥ n+min(i,n−i+l) + [log 2 (n)] − 4, for 2 ≤ i ≤ n−1, or, for the case of computing medians: f([n/2],n) ≥ 3n/2 − 3

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