Efficient and exact data dependence analysis
PLDI '91 Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation
Constraint-based array dependence analysis
Constraint-based array dependence analysis
Experience with efficient array data flow analysis for array privatization
PPOPP '97 Proceedings of the sixth ACM SIGPLAN symposium on Principles and practice of parallel programming
Constraint-based array dependence analysis
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Practical Decision Procedure for Arithmetic with Function Symbols
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Exact Method for Analysis of Value-based Array Data Dependences
Proceedings of the 6th International Workshop on Languages and Compilers for Parallel Computing
Independence of Negative Constraints
TAPSOFT '89/CAAP '89 Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming
Polynomial time array dataflow analysis
LCPC'01 Proceedings of the 14th international conference on Languages and compilers for parallel computing
An abstract domain extending difference-bound matrices with disequality constraints
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
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Constraint-based frameworks can provide a foundation for efficient algorithms for analysis and transformation of regular scientific programs. For example, we recently demonstrated that constraint-based analysis of both memory- and value-based array dependences can often be performed in polynomial time. Many of the cases that could not be processed with our polynomial-time algorithm involved negated equality constraints (also known as disequalities). In this report, we review the sources of disequality constraints in array dependence analysis and give an efficient algorithm for manipulating certain disequality constraints. Our approach differs from previous work in that it performs efficient satisfiability tests in the presence of disequalities, rather than deferring satisfiability tests until more constraints are available, performing a potentially exponential transformation, or approximating. We do not (yet) have an implementation of our algorithms, or empirical verification that our test is either fast or useful, but we do provide a polynomial time bound and give our reasons for optimism regarding its applicability.