On Approximating the Eigenvalues of Stochastic Matrices in Probabilistic Logspace

Dean Doron, Amir Sarid, Amnon Ta-Shma

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We show that approximating the second eigenvalue of stochastic operators is BPL-complete, thus giving a natural problem complete for this class. We also show that approximating any eigenvalue of a stochastic and Hermitian operator with constant accuracy can be done in BPL. This work together with related work on the subject reveal a picture where the various space-bounded classes (e.g., probabilistic logspace, quantum logspace and the class DET) can be characterized by algebraic problems (such as approximating the spectral gap) where, roughly speaking, the difference between the classes lies in the kind of operators they can handle (e.g., stochastic, Hermitian or arbitrary).

Original languageEnglish
Pages (from-to)393-420
Number of pages28
JournalComputational Complexity
Volume26
Issue number2
DOIs
StatePublished - 1 Jun 2017
Externally publishedYes

Keywords

  • Bounded space computation
  • Complete problems
  • Random walks
  • Randomized algorithms

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