Ignition in a stoichiometric acetylene-air mixture after a nanosecond surface dielectric barrier discharge was studied experimentally and numerically. Ignition was analyzed at 1 atm and 300 K by means of a high speed ICCD camera that allowed snapshot series in the microsecond time scale. Ignition delay time after the discharge and velocity of the combustion wave were measured for various electrode shapes, applied voltages and polarities. It was shown that the mixture is much easier to ignite by pulses of negative polarity and when the discharge develops from the cog-wheel-like electrode. The properties of the discharge were numerically simulated based on a 2D model. Using this model, the evolution in time of the spatial distributions of gas temperature and densities of active species produced in the discharge and in its afterglow was studied. The analysis of calculated results showed that the mixture is ignited due to active species production and local gas heating near the high-voltage electrode edge.