Implementing WS1S via finite automata

Abstract

It has long been known that WSIS is decidable through the use of finite automata. However, since the worst-case running time has been proven to grow extremely quickly, few have explored the implementation of the algorithm. In this paper we describe some of the points of interest that have come up while coding and running the algorithm. These points include the data structures used as well as the special features of the automata, which we can exploit to perform minimization very quickly in certain cases. We also present some data that enable us to gain insight into how the algorithm performs in the average case, both on random inputs and on inputs that come from the use of Presburger Arithmetic (which can be converted to WSIS) in compiler optimization.