INDUCTIVE COMPOSITION OF NUMBERS WITH MAXIMUM, MINIMUM, AND ADDITION: A New Theory for Program Execution-Time Analysis

Abstract

We extend the classic work of R.J. Parikh on context-free languages with operators min and max on unary alphabet. The new theory is called CAN (Compositional Algebra of Numbers) and can be used to model software processes that can be concatenated, concurrently executed, and recursively invoked. We propose and analyze an algorithm which constructs the execution time sets of a CAN in semilinear form. Finally, we consider several interesting variations of CAN whose execution time sets can be constructed with algorithms.