Detecting equality of variables in programs
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise interprocedural dataflow analysis via graph reachability
POPL '95 Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ACM Transactions on Programming Languages and Systems (TOPLAS)
Precise interprocedural dataflow analysis with applications to constant propagation
TAPSOFT '95 Selected papers from the 6th international joint conference on Theory and practice of software development
Propagating differences: an efficient new fixpoint algorithm for distributive constraint systems
Nordic Journal of Computing
The Value Flow Graph: A Program Representation for Optimal Program Transformations
ESOP '90 Proceedings of the 3rd European Symposium on Programming
A New Numerical Abstract Domain Based on Difference-Bound Matrices
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
The Interprocedural Coincidence Theorem
CC '92 Proceedings of the 4th International Conference on Compiler Construction
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Upper adjoints for fast inter-procedural variable equalities
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Checking herbrand equalities and beyond
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Interprocedural herbrand equalities
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Polyhedral analysis using parametric objectives
SAS'12 Proceedings of the 19th international conference on Static Analysis
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In this article we provide an interprocedural analysis of linear two-variable equalities. The novel algorithm has a worst-case complexity of 𝒪(n ⋅ k4), where k is the number of variables and n is the program size. Thus, it saves a factor of k4 in comparison to a related algorithm based on full linear algebra. We also indicate how the practical runtime can be further reduced significantly. The analysis can be applied, for example, for register coalescing, for identifying local variables and thus for interprocedurally observing stack pointer modifications as well as for an analysis of array index expressions, when analyzing low-level code.