citizenship test

If a taxpayers supports his/her parent who legally lives in the household for entire year than the parent is a resident alien as he./she meets the substantial presence test. Therefore, a parent can be claimed as exemption

Determining Alien Tax Status

If you are an alien (not a U.S. citizen), you are considered a nonresident alien unless you meet one of two tests. You are a resident alien of the United States for tax purposes if you meet either the green card test or the substantial presence test for the calendar year (January 1-December 31).

Based on the above IRS publication, a nonresident alien has to live with you the entire year in order to be able to claim as dependent. 183/184 days is only for green card holders or citizens.