It is a well established fact that adsorption of gas-phase molecules on metal surfaces changes the electronic properties of the adsorbates. An important consequence of this is the catalytic activity associated with the lowering of activation barriers which allows chemical reactions that do not occur in gas-phase to proceed rapidly on a surface. Adsorption systems and two-dimensional reactions are also very intriguing from the theoretical point of view, posing questions both on the level of electronic properties and on the level of the statistically defined ensemble of adsorbates. Specifically, it is of interest to study the spatial and temporal correlations that evolve in the adlayer. Due to the subtle interplay between many different interactions (the attachment to the surface, reactive annihilation between unlike species and the attraction/repulsion between like particles) that govern these systems the correlation patterns that evolve are very complex and are accessible mainly through Monte-Carlo simulations. Using such a simulation we focus here on correlations induced by the reactive interaction alone corresponding to the A + B → 0 annihilation reaction. This reaction induces complex aggregation-segregation patterns, even in the absence of interactions between the adsorbed particles.