THE AUSTRALIAN NATIONAL UNIVERSITY Second Semester 2019 COMP1600/COMP6260 (Foundations of Computation) Writing Period: 3 hours duration Study Period: 15 minutes duration Permitted Materials: One A4 page with hand-written notes on both sides Answer ALL questions Total marks: 100 The questions are followed by labelled blank spaces into which your answers are to be written. Additional […]
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Nondeterministic Finite Automata COMP1600 / COMP6260 Australian National University Semester 2, 2021 DFA Minimisation Elimination of equivalent states. if two states are equivalent, one can be eliminated Elimination of Unreachable States if a state cannot be reached from the initial state then it can also be eliminated. Example. S not reachable ?0 3
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Structural Induction COMP1600 / COMP6260 Australian National University Semester 2, 2020 1/60 Induction on Lists Q. How do we make all finite lists? A. All lists (over type A) can be obtained via the following: the empty list [] is a list (of elements of type A) given a list as and an element a
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First Order Logic COMP1600 / COMP6260 Australian National University Semester 2, 2020 First Order Natural Deduction: Example 1 ∀x(elephant(x) → happy(x)) 2 elephant(Appu) 3 elephant(Appu) → happy(Appu) 4 happy(Appu) ∀-E, 1 →-E, 2, 3 2/50 Natural deduction in first-order logic Proof rules for propositional natural deduction + quantifier rules: ∀-E universal elimination; ∀-I universal introduction;
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Recap – Course Structure This course includes 13 lectures and 10 tutorial/practical sessions Lecture 1 Introduction Lecture 2 Adv. topics&appl Lecture 3 Networks & Load Balancing Concepts Orchestration Storage Computation Others Programming and Linux experiences required! Lecture 4 VT: Docker I Lecture 5 VT: Docker II Lecture 6 VT: Docker III Lecture 7 DBs in
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COMP3012 – Compilers Coursework / Release date: Wednesday 10 November 2021 Submission deadline: 5 January 2022 Updates made after 10 Nov are written in red Contents 1 Description of the task 1 2 Instructions, help, and how to get started 2 3 Grammar of the Language 3 4 Extension of TAM 3 5 Variable Environment
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Propositional Logic COMP1600 / COMP6260 Australian National University Semester 2, 2021 This Course Programming. (Haskell, Java, Python, . . . ) Tell the computer how to perform a certain task Logic. (this course) Specify precisely what task should be performed Computation. (this course) the (discrete) maths of computation: what can be done in principle? You
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Hoare Logic: Partial Correctness COMP1600 / COMP6260 Australian National University Semester 2, 2021 Programming Paradigms Functional. (Haskell, SML, OCaml, . . . ) main paradigm: functions that don’t rely on state main ingredient: recursion Imperative. (C, Java, Algol, (Visual) Basic, . . . ) main paradigm: operations that do manipulate state. main ingredient: loops 1/51
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Turing Machines: Limits of Decidability COMP1600 / COMP6260 Australian National University Semester 2, 2021 Interlude: What can Haskell programs do? Observation. Turing machines ’recognise’ strings. Haskell functions of type String -> Bool also recognise strings. For a Haskell program p :: String -> Bool we can define L(p) = {w :: String | pw =
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Turing Machines COMP1600 / COMP6260 Australian National University Semester 2, 2021 1/45 (1912–1954) 2/45 2/45 Turing’s Scientific contributions 1936 introduces Turing machines and the study of computability 1950. introduces the Turing test that turns AI into a concrete research problem current today: Mitsuku, a computer programme has convinced judges (for the last 5 competitions –
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