The obvious question: What is an Assault Rifle?

According to Britannica Online Encyclopedia:

A military firearm that is chambered for ammunition of reduced size or propellant charge and that has the capacity to switch between semiautomatic and fully automatic fire. 

Some background: 

The key phrase in that definition is "switch between semiautomatic and fully automatic fire." Lets discuss these types of fire:

Semiautomatic fire: The weapon will perform all the necessary steps to reload and make the gun ready for fire every time the gun's trigger is pulled. Essentially, every time the trigger is pulled the gun fires 1 time and reloads for the next shot. It will not fire again until the trigger is released and pulled again.

Fully automatic fire: The weapon will fire repeatedly until the trigger is released or the feeding device (most cases this is a magazine) is empty. This is used primarily in military operations but even there it usually reserved for suppressing fire (a massive volley of fire to suppress the enemy). Fully automatic firearms, or machine-guns, in civilian hands are heavily regulated by two major pieces of legislation.

The first is the NFA act of 1934 which defined a machine gun to be any firearm capable of firing more than once for every trigger pull. i.e. a fully automatic firearm. There were many purposes of this law but in its essence it was designed to tax, curtail and track the transfer of the various types of firearms defined in the act, among them: machine-guns. [NFA]

The second was the Firearms Owners Protection Act (FOPA) which was enacted May 19th, 1986. This act sought to bring certain protections to firearms owners that travelled through and to different states in the nation. However, the Hughes amendment (H.AMDT.777) made it unlawful to transfer or possess a machine-gun if it was made after the enactment of the act. [H.AMDT.777]

So, lets simplify these two laws: on a federal level, it is legal for a civilian to possess a machine-gun if and only if he/she pays the applicable tax the machine-gun was manufactured and registered prior to May 19th, 1986. There is not much information on legally owned machine guns but some quick figures from GunCite and their sources show that:

• In 1995 there were 240,000 registered machine-guns in America distributed between civilian and different government entities (law enforcement for example).
• Only two crimes have been committed with legally own machine-guns since 1934.

But lets get back on topic:

The now infamous Bushmaster AR-15, and others like it, are not assault rifles given the above definition as they are only capable of firing in the semiautomatic mode. It is illegal, as per cited legislation, to modify these types of firearms to fire in the fully automatic mode.