• Publications
  • Influence
One-dimensional quantum walks
TLDR
A quantum analog of the symmetric random walk, which the authors call the Hadamard walk, is analyzed, which has position that is nearly uniformly distributed in the range after steps, in sharp contrast to the classical random walk.
Crossed and nested dependencies in German and Dutch
TLDR
This study investigates the consequences of differences in clause-final verbal clusters in Standard Dutch and German for the psycholinguistic processing complexity of sentences containing either crossed or nested dependencies and argues that the push-down stack is ruled out as the universal basis for the human parsing mechanism.
Explicit bounds for primality testing and related problems
Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits
Algorithmic Number Theory
Explicit bounds for primes in residue classes
TLDR
It follows from the proof that (1)-(3) also hold for arbitrary Galois extensions, provided the authors replace σ by its conjugacy class.
Analytic methods in the analysis and design of number-theoretic algorithms
  • E. Bach
  • Computer Science, Mathematics
  • 1985
This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic
Discrete Logarithms and Factoring
  • E. Bach
  • Computer Science, Mathematics
  • 1984
TLDR
Solving the discrete logarithm problem for a composite modulus is exactly as hard as factoring and solving it modulo primes.
Realistic analysis of some randomized algorithms
  • E. Bach
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1 January 1987
TLDR
The results below apply to sequences generated by iteratively applying functions of the form ƒ = &agr;&khgr; + &bgr; (mod p) to a randomly chosen seed x, and estimate the probability that a predetermined number of trials of an algorithm will fail.
An extension of classical transformational gram-mar
TLDR
Chomsky's latest papers (1976, 1975a: Ch. 3) assume that a modified 'intermediate structure' is transformed by rules of interpretation to a level of representation called 'logical form' (which is input to further rules).
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