Computability - Homepages | The University of Aberdeen
... History • Gottlob Leibnitz (1700) “Calculemus”: let’s decide all disputes by computation • David Hilbert (1900): “Can all questions of mathematics be answered algorithmically?” • Kurt Goedel (1931): This is not possible, even for number theory. (Result was independent of the notion of computation.) ...
... History • Gottlob Leibnitz (1700) “Calculemus”: let’s decide all disputes by computation • David Hilbert (1900): “Can all questions of mathematics be answered algorithmically?” • Kurt Goedel (1931): This is not possible, even for number theory. (Result was independent of the notion of computation.) ...
PPT
... Problem: Given an integer m, write a program that will find its smallest exact divisor other than 1. • Is the problem clear and well-defined? • what is a divisor? ...
... Problem: Given an integer m, write a program that will find its smallest exact divisor other than 1. • Is the problem clear and well-defined? • what is a divisor? ...
Solutions to Assignment 2.
... has half as many elements to compare. At the end only the global minimum will be left. This is n2 + n4 + n8 + . . . + 1 = n2 (2)(1 − n1 ) = n − 1 comparisons. Now, note that the second smallest element could only have been eliminated by the global minimum. Therefore, it must be one of the dlg ne ele ...
... has half as many elements to compare. At the end only the global minimum will be left. This is n2 + n4 + n8 + . . . + 1 = n2 (2)(1 − n1 ) = n − 1 comparisons. Now, note that the second smallest element could only have been eliminated by the global minimum. Therefore, it must be one of the dlg ne ele ...
chapter1
... Algorithm 1.4(matrix addition) n In some algorithms, the input sizes are measured by two numbers. The number of arcs and nodes in a graph ...
... Algorithm 1.4(matrix addition) n In some algorithms, the input sizes are measured by two numbers. The number of arcs and nodes in a graph ...
A Quick Overview of Computational Complexity
... in polynomial time by nondeterministic computers NP Include all problems in P The key question is are there problems in NP that are not in P or is P = NP? We don’t know the answer to the previous question But there are a particular kind of problems, the NP-complete problems, for which all known dete ...
... in polynomial time by nondeterministic computers NP Include all problems in P The key question is are there problems in NP that are not in P or is P = NP? We don’t know the answer to the previous question But there are a particular kind of problems, the NP-complete problems, for which all known dete ...
Countability
... The set of real numbers between 0 and 1 is uncountable Sketch: We will assume that it is countably infinite and then show that this is absurd. Assume we can list all the reals between 0 and 1 in a table as follows ...
... The set of real numbers between 0 and 1 is uncountable Sketch: We will assume that it is countably infinite and then show that this is absurd. Assume we can list all the reals between 0 and 1 in a table as follows ...
what is the asymptotic theory of repr
... What can we learn from the above problem? • In principle, for any question concerning representations of Sn there is a well-known answer given by some combinatorial algorithm. However, when n → ∞, such combinatorial answers are useless. We need more analytic methods. • In the asymptotic theory of r ...
... What can we learn from the above problem? • In principle, for any question concerning representations of Sn there is a well-known answer given by some combinatorial algorithm. However, when n → ∞, such combinatorial answers are useless. We need more analytic methods. • In the asymptotic theory of r ...
