Removing useless variables in cost analysis of Java bytecode

Automatic cost analysis has interesting applications in the context of verification and certification of mobile code. For instance, the code receiver can use cost information in order to decide whether to reject mobile code which has too large cost requirements in terms of computing resources (in time and/or space) or billable events (SMSs sent, bandwidth required). Existing cost analyses for a variety of languages describe the resource consumption of programs by means of Cost Equation Systems (CESs), which are similar to, but more general than recurrence equations. CESs express the cost of a program in terms of the size of its input data. In a further step, a closed form (i.e., non-recursive) solution or upper bound can sometimes be found by using existing Computer Algebra Systems (CASs), such as Maple and Mathematica. In this work, we focus on cost analysis of Java bytecode, a language which is widely used in the context of mobile code and we study the problem of identifying variables which are useless in the sense that they do not affect the execution cost and therefore can be ignored by cost analysis. We identify two classes of useless variables and propose automatic analysis techniques to detect them. The first class corresponds to stack variables that can be replaced by program variables or constant values. The second class corresponds to variables whose value is cost-irrelevant, i.e., does not affect the cost of the program. We propose an algorithm, inspired in static slicing which safely identifies cost-irrelevant variables. The benefits of eliminating useless variables are two-fold: (1) cost analysis without useless variables can be more efficient and (2) resulting CESs are more likely to be solvable by existing CASs.