Costs of General Purpose Learning

Leo Harrington surprisingly constructed a machine which can learn any computable function f according to the following criterion (called Bc∗ -identification). His machine, on the successive graph points of f, outputs a corresponding infinite sequence of programs p0, p1, p2, . . ., and, for some i, the programs pi, pi+1, pi+2, . . . each compute a variant of f which differs from f at only finitely many argument places. A machine with this property is called general purpose. The sequence pi, pi+1, pi+2, . . . is called a final sequence. For Harrington’s general purpose machine, for distinct m and n, the finitely many argument places where pi+m fails to compute f can be very different from the finitely many argument places where pi+n fails to compute f. One would hope though, that if Harrington’s machine, or an improvement thereof, inferred the program pi+m based on the data points f(0), f(1), . . ., f(k), then pi+m would make very few mistakes computing f at the “near fu...

• Type: Conference
• Year: 1999
• Where: STACS
• Authors: John Case, Keh-Jiann Chen, Sanjay Jain
• Keywords: Argument Places, Computable Functions, General Purpose, STACS 1999, Theoretical Computer Science