Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Asymptotically fast triangularization of matrices over rings
SIAM Journal on Computing
Discovering affine equalities using random interpretation
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
AMAST '02 Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology
Cleanness Checking of String Manipulations in C Programs via Integer Analysis
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise interprocedural analysis using random interpretation
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Analysis of modular arithmetic
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Grids: a domain for analyzing the distribution of numerical values
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
Interprocedurally analysing linear inequality relations
ESOP'07 Proceedings of the 16th European conference on Programming
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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In his seminal paper [5], Granger presents an analysis which infers linear congruence relations between integer variables. For affine programs without guards, his analysis is complete, i.e., infers all such congruences. No upper complexity bound, though, has been found for Granger's algorithm. Here, we present a variation of this analysis which runs in polynomial time. Moreover, we provide an interprocedural extension of this algorithm. These algorithms are obtained by means of multiple instances of a general framework for constructing interprocedural analyses of numerical properties. Finally, we indicate how the analyses can be enhanced to deal with equality guards interprocedurally.