Universal Algebra and Computational Complexity Lecture 3
Universal Algebra and Computational Complexity Lecture 3
Universal Algebra and Computational Complexity Lecture 3
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A variation: 1-SUB-MEM<br />
1-SUB-MEM<br />
This is the restriction of SUB-MEM to unary algebras (all fundamental<br />
operations are unary). I.e.,<br />
INPUT: A unary algebra A, a set S ⊆ A, <strong>and</strong> b ∈ A.<br />
QUESTION: Is b ∈ Sg A (S)?<br />
Here is a nondeterministic log-space algorithm showing 1-SUB-MEM ∈ NL:<br />
NALGORITHM: guess a sequence c 0 , c 1 , . . . , c k such that<br />
c 0 ∈ S<br />
For each i < k, c i+1 = f j (c i ) for some fundamental operation f j<br />
c k = b.<br />
Ross Willard (Waterloo) <strong>Algebra</strong> <strong>and</strong> <strong>Complexity</strong> Třešť, September 2008 10 / 31
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