Skip to main content Accessibility help
×
Home
Hostname: page-component-558cb97cc8-7xspw Total loading time: 0.298 Render date: 2022-10-07T20:30:01.171Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Linear logic and polynomial time

Published online by Cambridge University Press:  19 October 2006

DAMIANO MAZZA
Affiliation:
Institut de Mathématiques de Luminy (UMR 6206), Campus de Luminy, Case 907 – 13288 Marseille Cedex 9 Email: mazza@iml.univ-mrs.fr Homepage:http://iml.univ-mrs.fr/~mazza

Abstract

Light and Elementary Linear Logic, which form key components of the interface between logic and implicit computational complexity, were originally introduced by Girard as ‘stand-alone’ logical systems with a (somewhat awkward) sequent calculus of their own. The latter was later reformulated by Danos and Joinet as a proper subsystem of linear logic, whose proofs satisfy a certain structural condition. We extend this approach to polytime computation, finding two solutions: the first is obtained by a simple extension of Danos and Joinet's condition, closely resembles Asperti's Light Affine Logic and enjoys polystep strong normalisation (the polynomial bound does not depend on the reduction strategy); the second, which needs more complex conditions, exactly corresponds to Girard's Light Linear Logic.

Type
Paper
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
11
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org 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.

Linear logic and polynomial time
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Linear logic and polynomial time
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Linear logic and polynomial time
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *