TY - JOUR
T1 - Computation of recursive functionals using minimal initial segments
AU - Gordon, Dan
AU - Shamir, Eliahu
PY - 1983/5
Y1 - 1983/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=48749149483&partnerID=8YFLogxK
U2 - 10.1016/0304-3975(83)90036-1
DO - 10.1016/0304-3975(83)90036-1
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AN - SCOPUS:48749149483
SN - 0304-3975
VL - 23
SP - 305
EP - 315
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 3
ER -