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: 05 June 2012
The concept of a finite-state automaton has emerged as significant in many branches of human knowledge and understanding, including linguistics, computer science, philosophy, biology and mathematics.… In our work, finite-state automata are of fundamental importance: our objective is to use them to understand individual groups.
–from Word Processing in Groups [E+92]Regular Languages and Automata
We have explored the word problem about as far as is prudent without being a bit more careful with words like “decide” and “construct.” Here we introduce a standard mathematical model of computation. In thinking about modelling computation, there are a few key aspects that need to be preserved. One needs to have a way of inputing a sequence of information, and then a machine needs to execute various commands based on the input. One expects the total number of computations to be finite and possibly that there is some provision for the machine to have memory. The notion of finite-state automata, and their corresponding languages, fits these expectations.
Definition 7.1. Given an alphabet S = {x1, …, xn}, any subset of words in the free monoid on S, ℒ ⊃ S*, is a language.
There are numerous examples of languages. If S = {a}, then the set of all strings of even length, {a2n | n ∈ ℕ}, forms a language.
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.
