Should I aim at publishing a single-author paper on my PhD?
All of the doctoral work I'm most familiar with in CS has been published as single author work. You may want an extensive acknowledgements section if you have worked with others. There may be some corners of CS in which there is some division of labor, such as complicated data gathering v data analysis algorithmics that would be an exception, but I think that is still rare. 

Even in cases in which an advisor supplies the initial problem, it is fine in most of CS to publish as a single author. Mathematics is similar. It is in the lab sciences primarily that the standards are different as the very existence of the lab is essential as is collaboration with other lab people. 

But yes, speak to your supervisor and lay out your reasoning as here. You might even write up a draft that includes the ack section if you are far enough along. What you want to achieve, however, is a plan that makes everyone happy (enough) and leaves your advisor as a supporter of your work and future. 

But if you are in one of those subfields in which such multiple authorship is the norm, then your advisor should be able to convince you of that. 

But a rule of thumb might be the distinction between "I built this and you helped" vs "We built this together". There is a fuzzy area between them, of course. In general, though, it is best to know in advance which situation you will fall in to.