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- 1Briefly explain what Russell’s Paradox is.Cantor’s theory allowed a set R to be constructed of sets that are not elements of themselves, Russel’s paradox is that if R is an element of itself then it must satisfy the criteria to be in R, and if the set R is not an element of itself then it satisfies the condition to be in R.
- 2What is Gödel’s First Incompleteness Theorem? What does it say about Mathematics?Godels first incompleteness theorem shows that any formal axiomatic system for all of mathematics something can be proved even though it is false (inconsistent) and that there are statements that are true but can’t be proved (incomplete). He does this by constructing a statement “This statement is unprovable”, if the statement can be proved then it is inconsistent, if the statement can’t be proved then it is incomplete.
- 3What is the Entscheidungsproblem?The Entscheidungsproblem had been formulated by Hilbert in 1928: ‘Is there an algorithm that takes as input the description of a formal language and a statement in the language and produces as output true or false, depending upon whether the statement is true or false in the formal language?’
- 4What model of computation did Alan Turing come up with in order to try and understand what an algorithm is?Alan Turing came up with a simple model of computation that takes a string of symbols written on paper tape, the machine then applies a simple set of rules that decides which way to move along the paper tape depending on the state inside the machine and the input from the tape, decides whether to change the state of the machine, and whether to replace the current symbol.
- 5What is a universal Turing machine?It can do anything any other machine can do
- 6What is the Church-Turing Thesis?The Church-Turing thesis states that “Any function that is effectively computable can be computed by a Turing machine”, it is a thesis because it can never be proven (although it may one day be disproved).
- 7What does Turing-complete mean as regards a model of computation? Give a Turing-complete model of computation that is different to a Turing machine?A model of computation is called Turing complete if it can simulate any Turing machine. For example: Hao Wang’s Wang B-machines (1954)
- 8What is an unsolvable problem?An unsolvable problem is one that cannot be solved by a Turing machine, and assuming that the Church-Turing thesis is true, can therefore not be solved by any computer.
- 9Give an example of an unsolvable problem.The Wang tiles problem is an example of an unsolvable problem, given a finite set of square tiles with a colour on each of four edges can we tile an entire infinite plane with tiles ensuring that the edges of adjacent tiles are the same colour (and we have an infinite supply of tiles).
- 10Describe the Turing Test and explain what it is for.The Turing test is intended to decide whether or not a computer is intelligent, if a human speaking to the machine (via a screen and keyboard) can’t tell the difference between a machine and another human then the machine is considered intelligent.
- 11Give 3 objections to the Turing Test• A machine can’t have a soul, some people think that thinking is to do with something more than just the material and chemical reactions of the brain and that something else is needed for a person.
• The consequences of a machine ever passing the test could be severe, world taken over by AI kind of things, humans end up as slaves kind of thing.
• Machines are incapable of originality, since a machine has to be instructed to do everything you want from it. - 12What is the ACM Turing Award?The ACM Turing Award is kind of like computer sciences Nobel prize, it is awarded to “‘an individual selected for contributions of a technical nature made to the computing community. The contributions should be of lasting and major technical importance to the computer field”
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- Degree Engineering FlashCards sobre Sem título, criado por jeevanaujla97 em 30-05-2016.
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