Quasi-interpretations a way to control resources

This paper presents in a reasoned way our works on resource analysis by quasi-interpretations. The controlled resources are typically the runtime, the runspace or the size of a result in a program execution. Quasi-interpretations allow analyzing system complexity. A quasi-interpretation is a numerical assignment, which provides an upper bound on computed func-tions and which is compatible with the program operational semantics. Quasi-interpretation method offers several advantages: (i) It provides hints in order to optimize an execution, (ii) it gives resource certificates, and (iii) finding quasi-interpretations is decidable for a broad class which is relevant for feasible com-putations. By combining the quasi-interpretation method with termination tools (here term orderings), we obtained several characterizations of complexity classes starting from Ptime and Pspace.