Universal Algebra and Computational Complexity Lecture 3
Universal Algebra and Computational Complexity Lecture 3
Universal Algebra and Computational Complexity Lecture 3
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
An obvious upper bound for SUB-MEM<br />
Algorithm:<br />
INPUT: A, S, b.<br />
S 0 := S<br />
For i = 1, . . . , n ( := |A|)<br />
S i := S i−1<br />
For each operation f (of arity r)<br />
For each (a 1 , . . . , a r ) ∈ (S i−1 ) r<br />
c := f (a 1 , . . . , a r )<br />
S i := S i ∪ {c}.<br />
Next i.<br />
OUTPUT: whether b ∈ S n .<br />
n loops<br />
T operations<br />
≤ n r instances<br />
Heuristics:<br />
n (∑ f nar(f )) ≤<br />
n||A|| steps<br />
Ross Willard (Waterloo) <strong>Algebra</strong> <strong>and</strong> <strong>Complexity</strong> Třešť, September 2008 8 / 31
Change language