Difficult Problems
v There are a variety of kinds of problems that
computers “cannot” perform
; Some problems could be solved in principle, but it would
take so long and take so many resources that it is
impractical … simulating the positions of the stars in the
Milky Way galaxy over a million years
; Some problems cannot be solved because the inputs
and process determining the outcome cannot be known
… predicting today’s closing price for Amazon.Com
; Unsolvable problems cannot be computed … solving
them is logically inconsistent … a philosophically
interesting topic
The “halting problem” is a problem not solvable
by computer:  No program can tell if another
program will halt eventually or loop forever