Asking Questions Versus Verifiability

نویسندگان

  • William I. Gasarch
  • Mahendran Velauthapillai
چکیده

Inductive inference is the study of learning in a recursion-theoretic framework. The basic model is that the learner sees data f(0), f(1), . . ., makes conjectures e1, e2, . . . (these are programs) and eventually always outputs the same program, which is a program for f . This model was introduced by Gold [12]. This model, and several variants of it, have been extensively studied by several people including [2, 3, 16]. See [1, 10, 8] for several surveys. Case and Smith [3] studied learning machines whose conjectures are verifiable (i.e. the conjectures are total programs). They discovered that such machines are weaker then machines that are allowed to conjecture non-total programs (in symbols PEX ⊂ EX). Gasarch and Smith [9] studied machines that learn functions by asking questions about the function (see [6, 7] for subsequent work). They discovered that machines that can ask questions can usually learn more than machines that do not (in symbols EX ⊂ Q1EX[∗]). These two adjustments on the original model, and the results about them, lead to the following question: Can the weakness of verifiability be overcome by the strength of asking questions? While studying this question several other issues arise, including a more detailed study of verifiability.

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عنوان ژورنال:
  • Fundam. Inform.

دوره 30  شماره 

صفحات  -

تاریخ انتشار 1992