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.
from Part III - CHR programs and applications
Published online by Cambridge University Press: 10 February 2010
In this chapter, we present constraint solvers for constraints over variables that have infinite domains. The first domain is the numbers, and we solve linear polynomial equations. The second domain is some ordered set of values that we extend to a lexicographic order, which we consider as a constraint on a sequence of variables. The third domain is the objects that occur in knowledge representation with description logics. Reasoning in these logics is reducible to consistency checking. The fourth domain is the universal data structure of logical terms where we consider the unification problem as equation solving.
Linear polynomial equation solving
Typically, in arithmetic constraint solvers, incremental variants of classical variable elimination algorithms like Gaussian elimination for equations and Dantzig's Simplex algorithm for equations are implemented. Gaussian elimination has cubic complexity in the number of different variables in a problem. The Simplex algorithm has exponential worst-case time complexity but is polynomial on average.
Similar to Gaussian elimination, we solve linear polynomial equations by eliminating variables, one at a time. For solving inequations, the rules for Fourier's algorithm turn out to be very similar to those for equation solving.
Variable elimination
We define the syntax of the equations and show the principle of eliminating a variable.
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.
