Exact Results for Diffusion-Limited Reactions with Synchronous Dynamics

A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and certain correlation properties of these two reactions at all times. Asymptotic behavior at large times as well as scaling form describing the regime of low initial density, are derived explicitly.