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4.3 Examples

To illustrate the algorithm, consider the example problem in §3. It has n=m=2. With the assignments ordered according to the corresponding interger value, i.e., 00, 01, 10, and 11, tex2html_wrap_inline2130 where


The resulting behavior is:


giving an amplitude of 1 in the solution assignment 00.

Another example, with n=m=3 is the propositional formula (NOT tex2html_wrap_inline1708 ) AND (NOT tex2html_wrap_inline1710 ) AND tex2html_wrap_inline1712 , with assignments tex2html_wrap_inline2172 , represented as bit vectors, and solution tex2html_wrap_inline1714 , i.e., the bit vector 100. In this case U can be expressed in terms of tex2html_wrap_inline2178 from Eq. (15) in block form:


For this case, the algorithm's behavior is:


Again, all the amplitude is in the solution.

Tad Hogg
Feb. 1999