A note on logspace optimization

Abstract

We show that computing iterated multiplication of word matrices over {0,1}*, using the operations maximum and concatenation, is complete for the class optL of logspace optimization functions. The same problem for word matrices over {1}* is complete for the class FNL of nondeterministic logspace functions. Improving previously obtained results, we furthermore place the class optL in AC1, and characterize FNL by restricted logspace optimization functions.

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Àlvarez, C., Jenner, B. A note on logspace optimization. Comput Complexity 5, 155–166 (1995). https://doi.org/10.1007/BF01268143

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Key words

  • Complexity classes
  • nondeterministic logspace
  • optimization
  • iterated multiplication

Subject classifications

  • 68Q15
  • 68Q25