We study whether polycyclic aromatic hydrocarbons (PAHs) can be a weighty source of small hydrocarbons in photo-dissociation regions (PDRs). We modeled the evolution of 20 specific PAH molecules in terms of dehydrogenation and destruction of the carbon skeleton under the physical conditions of two well-studied PDRs, the Orion Bar and the Horsehead nebula which represent prototypical examples of PDRs irradiated by high and low ultraviolet radiation field. PAHs are described as microcanonical systems. The acetylene molecule is considered as the main carbonaceous fragment of the PAH dissociation as it follows from laboratory experiments and theory. We estimated the rates of acetylene production in gas phase chemical reactions and compared them with the rates of the acetylene production through the PAH dissociation. It is found that the latter rates can be higher than the former rates in the Orion Bar at $A_{rm V}<1$ and also at $A_{rm V}>3.5$. In the Horsehead nebula, the chemical reactions provide more acetylene than the PAH dissociation. The produced acetylene participate in the reactions of the formation of small hydrocarbons (C$_2$H, C$_3$H, C$_3$H$^{+}$, C$_3$H$_2$, C$_4$H). Acetylene production via the PAH destruction may increase the abundances of small hydrocarbons produced in gas phase chemical reactions in the Orion Bar only at $A_{rm V}>3.5$. In the Horsehead nebula, the contribution of PAHs to the abundances of the small hydrocarbons is negligible. We conclude that the PAHs are not a major source of small hydrocarbons in both PDRs except some locations in the Orion Bar.
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