What problems cannot Turing machines solve? Turing machine Undecidable problem A posi7ve example (algorithm) The corresponding Turing machine Turing machine wins PDA Turing NFA How to beat Turing machine? Turing machine ? Proof That Computers Can't Do Everything (The Hal7ng Problem) Watch this video h;ps://www.youtube.com/watch?v=92WHN-­‐pAFCs Bonus slide Proof by diagonaliza7on Diagonal Is recognizable? Cannot we help it to cheat? How to beat Turing machine? Turing machine ? How to beat Turing machine? Turing machine HalGng problem Proof That Computers Can't Do Everything (The Hal7ng Problem) Watch this video again at home. h;ps://www.youtube.com/watch?v=92WHN-­‐pAFCs Quiz: blue print? The class of decidable languages is a sub-­‐class of recognizable languages Recognizable languages Decidable Languages The class of regular languages is a sub-­‐class of context-­‐free languages The hierarchy of languages so far Recognizable languages Decidable Languages Interes7ng to see the hierarchy in a “finer resolu7on” Recognizable languages ? Decidable Languages Complexity theory