In this thesis we deal with the problem of temporal logic robustness estimation. We present a dynamic programming algorithm for the robust estimation problem of Metric Temporal Logic (MTL) formulas regarding a finite trace of time stated sequence. This algorithm not only tests if the MTL specification is satisfied by the given input which is a finite system trajectory, but also quantifies to what extend does the sequence satisfies or violates the MTL specification. The implementation of the algorithm is the DP-TALIRO toolbox for MATLAB. Currently it is used as the temporal logic robust computing engine of S-TALIRO which is a tool for MATLAB searching for trajectories of minimal robustness in Simulink/ Stateflow. DP-TALIRO is expected to have near linear running time and constant memory requirement depending on the structure of the MTL formula. DP-TALIRO toolbox also integrates new features not supported in its ancestor FW-TALIRO such as parameter replacement, most related iteration and most related predicate. A derivative of DP-TALIRO which is DP-T-TALIRO is also addressed in this thesis which applies dynamic programming algorithm for time robustness computation. We test the running time of DP-TALIRO and compare it with FW-TALIRO. Finally, we present an application where DP-TALIRO is used as the robustness computation core of S-TALIRO for a parameter estimation problem.