Turing Machines are in turn correspond to lambda calculus, from what we can conclude that all computable problems are function-based. This is not quite correct. Some computer scientists think an algorithm is a function from inputs to outputs. If that were true, then bubble sort and heap sort...
To summarise, based on this view a function is computable if: (a) given an input from its domain, possibly relying on unbounded storage space, it can give the corresponding output by following a procedure (program, algorithm) that is formed by afinite number of exact unambiguous instructions;...
important to come up with appropriate algorithms for taking uncertainty into account.Before we concentrate our efforts on designing such algorithms, it is important to make sure that such an algorithm is possible in the first place, i.e., that the corresponding problem is algorithmically computable...
flow of control process that specifies when each step is executed a means of determining when to stop 1 + 2 + 3 = an algorithm! BASIC MACHINE ARCHITECTURE 基本机器架构基本机器架构 例如要计算1+2和3+4,数据是1,2,3,4,基本操作是+,从内存输入以上内容到控制单元(CONTROL UNIT),也就是程序计数器...
e.g.,additionandmultiplication)arecomputablefunctions.Forafunctiontobecomputable,itmustadmitofanalgorithm.Analgorithmisastep-by-stepmechanicalprocesswhich,iffollowedfaithfully,isguaranteedtoproducethecorrectoutput(the"answer")foranyinput.Therulesthatacalculatorfollowswhenitperformsarithmeticareallalgorithms....
How do you know that one program is more efficient than the other?How do you know that one algorithm is better than the other?That's what we're going to talk about in the last part. Let's start by talking at a high level what does a computer do. Fundamentally,it does two things....
the Turing machine program he is carrying out is an implementation of the Euclidean algorithm. His instructor, looking at the pages of more or less meaningless computations handed in by the student, can tell from them that the greatest common divisor of 24 and 56 is 8. The student, not kno...
A non-computable is a problem for which there is no algorithm that can be used to solve it. Most famous example of a non-computablity (or undecidabilityundecidabilityIn
Once you've figured out what the various problems are, you need to figure out how you can solve each one, within the limitations of what a computer can do, using a logical series of clearly defined steps called analgorithm. Programmers often figure out their algorithms by drawingflowcharts,...
all prime factors are at most ), then by the greedy algorithm one can find a divisor of with ; if we set , then , and the above proposition then gives which can improve upon the Burgess bound when is small. For instance, if , then this bound becomes ; in contrast the Burgess ...