Everyone is familiar with the \Omega(n \log n) lower bound on sorting 
that can be obtained using a decision tree argument. Now consider the 
following "Element Uniqueness" problem: Are any two elements of the 
sequence (x_1, x_2, ..., x_n) equal? The same information-theoretic 
argument does not work for proving a lower bound for this problem --- 
there are only two possible outputs "Yes" and "No". We will discuss 
linear and algebraic decision trees that allow one to answer 
questions about the lower bounds on problems such as the one posed 
above.