Computation of recursive functionals using minimal initial segments

Dan Gordon, Eliahu Shamir

Research output: Contribution to journalArticlepeer-review


The following problem in the computation of partial recursive functionals is considered: Minimizing the length of initial segments of input functions containing all function values requested by a machine computing a partial recursive functional. A recursive functional F is constructed such that any algorithm for F has unbounded redundancy, i.e. it requests function values on inputs unboundedly larger than those on which the output of F depends. However, for any recursive functional F such that the length of the segment on which F depends is itself a recursive functional, a non-redundant machine for F can be effectively constructed. Also considered are machines on 0-1 sequences for which it is shown that a machine realizing a given level of significance in a universal test of randomness must have unbounded redundancy.

Original languageEnglish
Pages (from-to)305-315
Number of pages11
JournalTheoretical Computer Science
Issue number3
StatePublished - May 1983

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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