Upper bounds for the complexity of sparse and tally descriptions

  title={Upper bounds for the complexity of sparse and tally descriptions},
  author={Vikraman Arvind and Johannes K{\"o}bler and Martin Mundhenk},
  journal={Mathematical systems theory},
We investigate the complexity of computing small descriptions for sets in various reduction classes to sparse sets. For example, we show that if a setA and its complement conjunctively reduce to some sparse set, then they also are conjunctively reducible to a P(A ⊕ SAT)-printable tally set. As a consequence, the class IC[log,poly] of sets with low instance complexity is contained in theEL 1 Σ -level of the extended low hierarchy. By refining our techniques, we also show that all word-decreasing… CONTINUE READING

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