Is it acceptable for a student to ask a professor to be included as a co-author on the professor's paper?

It's fine to just ask.

But if you feel uncomfortable asking straight out "Can I be considered for authorship on this paper?" an alternative approach is to have a conversation about authorship that (1) makes it clear to the professor that you're interested in authoring a research paper, and (2) helps you understand the shades of "it depends" for your specific kind of research.

For example, you might bring up in conversation:

In our field, what kind of contribution are students expected to make in order to merit authorship on the paper that comes out of their work?

Then you can ask,

On this project, what additional work could I have done in order to have sufficient contribution to be considered an author?

and then, if you want very much to co-author a research paper and plan to continue working with this professor,

I'm interesting in being a co-author on a research paper. On the next project we work on, can I have a role that (if I do it well) merits co-authorship?

Ideally, if you had just asked straight out "Can I be considered for authorship on this paper?", the ensuing discussion would also cover the points above.

Your question is a fantastic example of why the best time to have these discussions is BEFORE you start to work on a project with a professor or a grad student (I'm assuming you are an undergrad). Now, you are in an awkward situation where you did a ton of work and you feel as though you should be rewarded for it, but you don't want to jeopardize the relationship with the professor. Chances are, if you ask for authorship, the professor will say no, and you may feel slighted, and they may feel put upon by the question (although probably not). The point is, it's just discomfort all around on what should be a high note for what sounds like a successful project.

I am not saying this to scold you in any way. You really could not have been expected to think of this beforehand. But in the future, you'll know to have the talk before doing any work, so that expectations are clear. I think that people who mentor undergraduates that participate in research should do better in preparing them for these situations so that they are neither exploited nor put in a position of feeling exploited when they were not.

As to your particular situation, I don't know what the authorship norms are in your field, but in my field (natural/behavioral sciences), your work does not constitute authorship. You did not design the project, get funding for it, conduct analysis, etc. You were a tech. That doesn't mean what you did wasn't important or valuable. Techs are often indispensable, but they don't get authorship for that. I know that may seem unfair when sometimes people are given authorship simply for allowing the use of their lab without being involved, but...them's the perks of being the PI, kid.

Now, you should absolutely be included in the acknowledgements section of the paper. If you're not, that's really an oversight. If you want to give your professor a nudge to make sure you're included there, that would be perfectly fine.

Is it acceptable for a student to ask a professor to be included as a co-author on the professor's paper?

The literal answer to this is sure, it's acceptable. Though I think that typically if you have to ask, you probably shouldn't... This isn't a universal rule; just a generalization. In my experience, professors really do want the best for their students and so if a student genuinely assisted with the research, professors will rightfully include them as a coauthor. In other words, the likelihood of a professor just "forgetting" to recognize you as a coauthor or being ignorant to your research on the project is slim to none.

However, I did not perform any actual research

If this is the case, I find it quite difficult to justify why your name should be on the research paper. But, if the following is true

though without my work, their research likely would not have been possible

then I don't see it as unreasonable to be asked to be mentioned in the paper itself when they described the unique software that they used to get the research done. I highly doubt that they wouldn't mention you in the body of the document if your software is as pivotal to their research as you say- but to credit you on their research as a coauthor is a bit too generous (as well as nonacademic) if you genuinely didn't assist with the research process.

Did you push the boundaries of modern computer science in the pursuit of writing the program that they used? Did you yourself perform ground breaking research to make the program function? If so, then you deserve to take the time to draft your own research paper. (I'm being serious. Contact a CS adviser immediately.)

If not, then the idea of crediting you on their research is analogous to the programmers of LaTeX requiring their authorship by anyone who uses their software to draft research papers.