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Entailment with Conditional Equality Constraints

Summary: Entailment with Conditional Equality
Zhendong Su and Alexander Aiken
EECS Department, University of California, Berkeley
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
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 well-known 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


Source: Aiken, Alex - Department of Computer Science, Stanford University
Su, Zhendong - Department of Computer Science, University of California, Davis


Collections: Computer Technologies and Information Sciences