How Hard Can a Problem Be ?

How Hard Can a Problem Be ? Ahmad Saeed Alexandria University

Agenda ,[object Object],[object Object],[object Object],[object Object]

A Problem Solver (Turing Machine) ,[object Object],[object Object],[object Object],[object Object]

Turing Machines Formally ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Turing Machine Example ,[object Object],[object Object],[object Object]

Church-Turing Thesis ,[object Object]

"Easy" Problems (P) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Nondeterminism (Example) ,[object Object]

"Hard" Problems (NP) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Can all problems be solved by a computer ??

Halting Problem ,[object Object]

Halting Problem Proof ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What have we been talking about ?? ,[object Object],[object Object],[object Object]

References ,[object Object],[object Object],[object Object],[object Object]

Any Questions ?? (Open Discussion)

Thank you for hanging around!! Ahmad Saeed www.ahmad-saeed.co.cc [email_address]

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