Under 17 USC 101, "perform" is defined as:
To “perform” a work means to recite, render, play, dance, or act it,
either directly or by means of any device or process or, in the case
of a motion picture or other audiovisual work, to show its images in
any sequence or to make the sounds accompanying it audible.
To display is:
To “display” a work means to show a copy of it, either directly or by
means of a film, slide, television image, or any other device or
process or, in the case of a motion picture or other audiovisual
work, to show individual images nonsequentially.
The terms "display" and "perform" do not apply to what one ordinarily does with software. Software isn't an audiovisual work so the second half of the definition of "perform" is inapplicable. You also can't recite, render, play, dance, or act software -- you can run / execute it, and that isn't part of what "perform" means. Likewise you don't display software when you execute it – you might display a thing created by software, but you don't (usually) display the software itself.
There are competing legal theories (held by judges) about how to interpret laws. One approach pays attention to the literal meaning of words, and in that approach one cannot say that running software constitutes "performance" or "display". Another approach is to decide what the outcome is supposed to be in a given case, and then stretch the meaning of words (or not) to fit that end. You might guess I don't like the latter approach: I mention this because it's not inconceivable that the meaning of "perform" could be stretched to mean "execute", given a bit more shift in judicial philosophy.
But notice that section 106 (4)-(6) specifically ties "performance" to literary, musical, dramatic, and choreographic works, pantomimes, and motion pictures and other audiovisual works" as well as sound recordings, and ties "display" to "literary, musical, dramatic, and choreographic works, pantomimes, and pictorial, graphic, or sculptural works, including the individual images of a motion picture or other audiovisual work". In other words, we don't need to care about "perform" and "display" because performing softward and displaying software is not a protected right anyhow, at least by the letter of the law.
Using software at all without permission is prohibited, even in the privacy of your own home. To use software, it has to be copied (which you can't legally do without permission). Copyright law is mostly irrelevant to questions of software, and what really controls what you can and cannot do is the license agreement. Because of copyright law, you can't say "But this was an unlicensed usage so I'm not bound by those terms", so copyright law provides the Scylla and the license provides the Charybdis.
17 USC 117 says:
it is not an infringement for the owner of a copy of a computer
program to make or authorize the making of another copy or adaptation
of that computer program provided:
(1) that such a new copy or adaptation is created as an essential step
in the utilization of the computer program in conjunction with a
machine and that it is used in no other manner
Installing (copying) sure enough is an essential step in utilization. This slice of code suggests that you can use the software, given copyright law. But that would be so only if you are the owner of a copy of the program, and one often does not buy a copy of the program, one buys a license, if you are to believe what the license says.
In Vernor v. Autodesk, the court held that customers are "licensees of their copies of the software rather than owners" (so Vernor did not buy his copy from an owner). One reason why Autodesk ultimately prevailed is that they asserted in the license that they retain title (they lost in the lower court, Vernor v. Autodesk, 555 F. Supp. 2d 1164). Similarly, the Office 2007 license says "The software is licensed, not sold", thus closing any arguments that you can do things not permitted by the license. The point being, if you don't own the software, you can't execute it in public, unless the license allows it.
If you do own the software, then we can turn to questions of what copyright law might allow. In order to prevent you from publicly running software, the act would have to be something prohibited by copyright law -- like making a copy. the degree of copying involved in installing / executing software would be allowed by section 107, and there is no statutory restriction on public "use" except that which is limited to literary, musical etc. works. At present, software is not considered to be a "literary work" or similar, therefore there is no statutory basis for prohibiting the public execution of a piece of software. Any such limitations must derive from the license agreement.
