GaAs has high three photon absorption (3PA) co-efficient at mid-infrared wavelength like2.2mm and waveguides can be formed with this material like silicon nano-wires. It is shown that three-photon-absorption in GaAs wire waveguide can be utilized to form NAND gate. Three-photon-absorption is incorporated in one-dimensional Finite Difference Time Domain (FDTD) equations. The evolution of a probe pulse under the influence of a pump pulse through crossabsorption in a waveguide is investigated using FDTD simulation, where the dominant process is nonlinear three-photon-absorption. Output probe power dependence on input pump power shows that GaAs waveguide NAND gate has higher extinction ratio in comparison to NAND gate using two-photon-absorption in silicon waveguide.