University of Sussex Informatics Spring 2021 Limits of Computation Exercises 2 (covers Lectures 3–5) WHILE-programs: Syntax & Semantics and Extended WHILE 1. Consider the binary tree t, given in linear notation: ⟨ ⟨ ⟨ nil.nil ⟩.nil ⟩.⟨ ⟨ nil.nil ⟩.nil ⟩ ⟩ (a) Draw t in the usual two-dimensional form. (b) Does t encode a […]
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University of Sussex Informatics Spring 2021 p1 read L { R := 0; X := hd L; Y := hd tl L; while X { R := [ Y, R ]; X := tl X } } write R Figure 1: WHILE-program p1 WHILE add read L { X := hd L; Y := hd
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Limits of Computation 7 – A universal program (Self-interpreter) Bernhard Reus 1 So far… • … we have learned the WHILE-language… • …that we have chosen to represent our notion of computation (to write “effective procedures”). • We learned how to represent programs-as- data… • …so now we can write interpreters. 2 • Eating your
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Limits of Computation 2020/21 Notes on Lectures 1–4 ⃝c Dr Bernhard Reus, University of Sussex January 27, 2021 1 Introduction (and module outline) As final year undergraduate (or postgraduate) students you will know how a modern digital computing device works. You know about these gadgets’ archi- tecture, their operating systems, their input/output devices, their networking
Limits of Computation 10 – Partial evaluation & self-referencing programs Bernhard Reus 1 So far … • … we have seen how programs can be encoded as objects to be used as input to other programs. • Example: self-interpreter to show semi- decidability of Halting Problem. 2 Question: Can we write a Java program that
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University of Sussex 4 May 2018 Limits of Computation Test →a→→→→→→→→→ → → CandidateNo. • Please answer ALL questions by writing on THIS SHEET. You are not allowed to use any other documents or devices. • Please write your candidate number in the box above. • Questions are equally weighted (but Q1 – Q2 which
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The National Student Survey (NSS) 2021 Have your say 1 Have your say What is the NSS? A national survey of all final-year undergraduate students. It’s designed to find out about your experience of studying at Sussex When does the survey run? The NSS opened on 6 January and closes on 30 April 2021 Why
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University of Sussex Informatics Spring 2021 Limits of Computation Feedback to Exercises 2 (covers Lectures 3–5) Dr Bernhard Reus WHILE-programs: Syntax & Semantics and Extended WHILE 1. Consider the binary tree t in linear notation: ⟨ ⟨ ⟨ nil.nil ⟩.nil ⟩.⟨ ⟨ nil.nil ⟩.nil ⟩ ⟩ (a) Draw t in the usual two-dimensional form. Answer
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Limits of Computation 2020/21 Notes on Lectures 5–8 Dr Bernhard Reus February 13, 2021 5 WHILE-Extensions The WHILE-language was simple enough to give it a precise semantics in the previous chapter. Accordingly, we adopt it as our language to write “effective procedures”. Nevertheless, it turns out that some language features not included in WHILE make
Limits of Computation 8 – Our first non-computable problem Bernhard Reus 1 A non-computable problem THIS TIME • • we consider a decision problem: the Halting Problem, and prove it is WHILE- undecidable! Deep Thought we define formally what computability and decidability means (for WHILE) “What is the Ultimate Answer to Life, the Universe, and
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