We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 26 October 2011
“Theory of computation begins with alphabets and flows as poetry in mathematical rhythms.”
Introduction
When we study computability, we study problems in an abstract sense. For example,
a. Addition is the problem of returning a third number that is the sum of two given numbers.
b. Travelling Salesman problem (TSP) is one in which a list of distances between some number of cities are given and the person is asked to find the shortest route so that he visits each city once and returns to the start.
c. Halting Problem (HP) is one in which a program is given some appropriate input and it needs to be decided whether the program, when run on that input, loops forever or halts.
Problems (b) and (c) are the two problems of computer interest.
In both these problems, the statement of the problem does not give the actual values needed to provide the result but just tells what kind of objects they are. A set of actual values for a problem is called an instance of the problem (by this terminology, all homework problems done by school students are considered as instances of problems).
In all these problems an instance is required that is the input and the relationship between the input and the output is to be understood. In order to solve these problems, there are certain things one should know.
Can it be solved algorithmically – is there any definite procedure that solves any instance of the problem in a finite amount of time? In other words, is it computable? Not all problems are computable.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
