Is it possible to write a program to solve Nonograms? Well, of course it is. And there are many approaches, as can be seen from the links on Steven Simpson's Nonograms site.
The solver given here works methodically, trying each row and each column in turn, using the techniques given in the tutorial. You can run it one step at a time, to follow how it calculates, or just run it continuously to watch the picture build up.
This example shows the solver working on a competition puzzle, published by the Daily Telegraph in the UK over Christmas.