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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Size of an algebra<br />
Define some parameters:<br />
||A|| = ∑<br />
fund f<br />
(<br />
)<br />
n arity(f ) log n + 1 .<br />
R = maximum arity of the fundamental operations (assume > 0)<br />
T = number of fundamental operations (assume > 0).<br />
Then<br />
n R log n ≤ ||A|| ≤ T ·n R log n + T .<br />
In particular, if we restrict our attention to algebras with some fixed<br />
number T of operations, then<br />
||A|| ∼ n R log n.<br />
Ross Willard (Waterloo) <strong>Algebra</strong> <strong>and</strong> <strong>Complexity</strong> Třešť, September 2008 4 / 31
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