程序代写 COSC1107 Computing Theory

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[Content_Types].xml

Click to edit the title text format Click to edit the outline text format Second Outline Level Third Outline Level Fourth Outline Level Fifth Outline Level Sixth Outline Level Seventh Outline Level Eighth Outline Level Ninth Outline Level <> Computing Theory ‹#›

COSC1107 Computing Theory (We will commence soon. We are just allowing a few minutes for people to join and set up. Please mute your microphone unless you are speaking . You can raise your hand or use the chat at any time.) ppt_x ppt_y

COSC1107 Computing Theory Complexity & Intractability Week 9 Week 9 Computing Theory * With thanks to Intro music ‘Far Over’ playing now … style.visibility ppt_x ppt_y ppt_x ppt_y style.visibility

Acknowledgement Week 9 Computing Theory RMIT University acknowledges the people of the Woi wurrung and Boon wurrung language groups of the eastern Kulin Nations on whose unceded lands we conduct the business of the University. RMIT University respectfully acknowledges their Ancestors and Elders, past and present. RMIT also acknowledges the Traditional Custodians and their Ancestors of the lands and waters across Australia where we conduct our business. (add your name here to volunteer for this or email me) (my personal Acknowledgement of Country is here )

Overview Questions? Computational Limits Questions? Measuring Complexity Questions? Intractable problems Questions? Platypus Game Questions? Week 9 Computing Theory Of course! style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y

Questions? Questions? Questions? Week 9 Computing Theory

Computing Theory topics Week 9 Computing Theory {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} Languages What do you want to do? Grammars What can you say? Automata What can you do? Computability What can’t you do? Complexity How hard can it be? Any attempt to solve an undecidable problem must be incomplete Sometimes ‘yes’ Sometimes ‘no’ Sometimes ‘maybe ’ Cannot be eliminated! Any such attempt can only be an approximate solution style.visibility style.visibility

Computational limits Week 9 Computing Theory There are various limits on computation Technological Any computing device has a finite memory, storage capacity, processing speed, bandwidth, … There is always a problem “just beyond” any technology Example: Platypus tournament Practical (Complete) Algorithmic solutions exist Complexity is too high for problems beyond a smallish size Example: Hamiltonian circuit problem Fundamental No (complete) algorithmic solutions exist Will always be beyond any technology Example: Halting problem style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y style.visibility ppt_w ppt_h style.rotation

Computational limits Week 96 Computing Theory Within current technology Beyond current technology but feasible Beyond any technology but decidable Beyond any algorithm ever Undecidability Intractability Technology All processing power is finite! style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y style.visibility ppt_x ppt_y style.visibility

Computational limits Week 9 Computing Theory Within current technology Beyond current technology but feasible Beyond any technology but decidable Beyond any algorithm ever Undecidability Intractability Technology Asymptote! (can never be reached)

Complexity Computing Theory Week 9 Finite state machines Regular even 1’s Context-free wcw R ND Pushdown automata Linear bounded TM Context sensitive a n b n c n Turing machines Unrestricted {( M,w )|M accepts w} Undecidable Undecidable Halting problem L(G) = Σ ∗   L(G 1 ) = L(G 2 ) Decidable problems How hard can they b

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