combustion - What is the oxidation mechanism of gunpowder?

I've been recently looking into fireworks and the chemistry of explosives, and I found out that, amongst others, one of the most important reactions in gunpowder ignition is the oxidation of charcoal and sulfur by $\mathrm{KNO_3(s)}$. I am curious as to whether it is known if this reaction occurs between charcoal/sulfur and solid state potassium nitrate or if the potassium nitrate decomposes first and the reaction occurs via gaseous oxygen as an intermediate.

Is there a general mechanism of oxidation between solid oxidizing salts and organic matter/sulfur? Does the same thing happen with $\mathrm{KClO_3(s)}$ or $\mathrm{KMnO_4(s)}$ for example?