Matching guitar signal with tablature, near real-time algorithms?
Assuming that the tablature is well defined; let's say it's a MIDI file complete with pitch bend commands.  you can make a synthesizer where each note is actually a tracking comb filter tuned to the midi note (and offset by the pitch bend command) with notches at each integer harmonic (including the fundamental).  if those tracking comb filters processes a sound file playing that MIDI file and the two are properly aligned in time, the tracking comb filters should null out most of the input audio, even polyphonic.

Then magnitude-square-LPF the result and a minimum value means a pretty good match.

Just an idea.  No equations, but I have posted about pitch detection before. And I thought I did about tuned comb filters, too (you need a precision delay line to tune the comb filter to whatever fine-tuned pitch that is specified).