The 2-tag Halting Problem
This version of the halting problem is among the simplest, most-easily described undecidable decision problems:
Given an arbitrary positive integer n and a list of n+1 arbitrary words P1,P2,...,Pn,Q on the alphabet {1,2,...,n}, does repeated application of the tag operation t: ijX → XPi eventually convert Q into a word of length less than 2? That is, does the sequence Q, t1(Q), t2(Q), t3(Q), ... terminate?
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Famous quotes containing the words halting and/or problem:
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“It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.”
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