CS代考 COSC1107 Computing Theory

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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 Computability, Universality Week 5 Week 5 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 5 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)

Overview Questions? Universal Turing Machines Questions? Computability Questions? Platypus Game Questions? Week 5 Computing Theory What can be done What can’t be done Both! style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility

Questions? Questions? Questions? Week 5 Computing Theory

Church-Turing thesis Week 5 Computing Theory No need to seek anything more powerful (there is nothing!) Enables rigorous analysis of computation Can’t be done by a TM means can’t be done at all! Thesis, not a theorem Observed property of the universe, like scientific laws Consistent with observation, no counterexamples known so Turing machines are adequate for anything that can be computed Church-Turing thesis (1936) Any computation can be translated to an equivalent computation on a Turing machine style.visibility ppt_x ppt_y

Church-Turing thesis Week 5 Computing Theory “A man * provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.” — “The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer.” — “It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with a tape on the beginning of which is written the [encoding] of some computing machine M ,then U will compute the same sequence as M.” — * This now sounds very dated. But that is what he said back in the 1930’s …

Church-Turing thesis Week 5 Computing Theory {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} Model of computation Description enhanced Turing machines multiple heads/tapes, 2D tape, nondeterminism untyped lambda calculus method to define and manipulate functions recursive functions functions dealing with com

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