Summary: The Complexity of Set Constraints \Lambda
Alexander Aiken 1 , Dexter Kozen 2 , Moshe Vardi 1 , Ed Wimmers 1
1 IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA
2 Computer Science Department, Cornell University, Ithaca, NY 14853, USA
Abstract. Set constraints are relations between sets of terms. They have
been used extensively in various applications in program analysis and type
inference. We present several results on the computational complexity of
solving systems of set constraints. The systems we study form a natural
complexity hierarchy depending on the form of the constraint language.
Systems of set constraints have received considerable attention as a formalism for
expressing algorithms in program analysis and type inference. Many algorithms
based on set constraints have been proposed and implemented, but very little is
known about the computational complexity of solving systems of set constraints.
In this paper we present complexity results for a natural hierarchy of decision
problems involving set constraints.
Set constraints are formal inclusions between expressions representing subsets
of T \Sigma , the set of ground terms over a finite ranked alphabet \Sigma . A positive set