To answer your question on this forum without a thorough check of your records would be irresponsible at best. What you should do is show your records to an attorney and have the attorney evaluate (based on the terms of your probation, the actual statute that you were charged under, the underlying facts of the case) whether a naturalization application would be in your best interest.
Also remember the following:
1) Naturalization applications involve a very thorough background check for criminal background.
2) Taxes are scrutinized
3) Your past applications, including your applications for green card can be re-examined and worst case scenario you may even lose your green card as a result.
You should get an evaluation done for your application. It is one of the services we offer our clients with varying rates depending on what exactly is required. Good luck!
Simple battery is not a crime of moral turpitude. If this is your only crime, then you should be eligible to apply for naturalization.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.