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Nicki Minaj[1]'s husband really wants to get back to surfing the Internet ... something he's currently barred from doing due to his pending criminal case.

Kenneth Petty[2] just submitted legal docs, obtained by TMZ, begging a California judge to allow him to use the World Wide Web.

imageDepartment of Justice

As you know ... Kenneth recently registered as a sex offender[3] in Cali after getting arrested[4] for allegedly failing to do so when he moved to the state with Nicki. One of the terms of his pretrial release -- he can't use the web unless approved by a supervisor.

According to the docs, prosecutors have already agreed to Kenneth's request ... so now, it's up to the judge to sign off.

BTW ... Petty's status as a sex offender stems from a 1995 New York conviction for first-degree attempted rape.[5]

Kenneth, who pled not guilty to failing to register as a sex offender, has a curfew and is being required to wear an ankle monitor as he waits for next month's court date. His travel is also restricted to Southern California.

Sounds pretty boring ... especially offline.

Read more from our friends at TMZ