 
Summary: Entailment with Conditional Equality
Constraints
Zhendong Su and Alexander Aiken
EECS Department, University of California, Berkeley
{zhendong,aiken}@cs.berkeley.edu
Abstract. Equality constraints (unification constraints) have
widespread use in program analysis, most notably in static poly
morphic type systems. Conditional equality constraints extend equality
constraints with a weak form of subtyping to allow for more accurate
analyses. We give a complete complexity characterization of the various
entailment problems for conditional equality constraints. Additionally,
for comparison, we study a natural extension of conditional equality
constraints.
1 Introduction
There are two decision problems associated with constraints: satisfiability and
entailment. For the commonly used constraint languages in type inference and
program analysis applications, the satisfiability problem is now well under
stood [1, 2, 8, 11, 16, 17, 20, 22, 23, 7, 6, 27]. For example, it is wellknown that
satisfiability of equality constraints can be decided in almost linear time (linear
time if no infinite terms are allowed [21]). For entailment problems much less is
