Theory of linear and integer programming
Theory of linear and integer programming
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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 widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
A generic framework for interprocedural analysis of numerical properties
SAS'05 Proceedings of the 12th international conference on Static Analysis
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The gauge domain: scalable analysis of linear inequality invariants
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Polyhedral analysis using parametric objectives
SAS'12 Proceedings of the 19th international conference on Static Analysis
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In this paper we present an alternative approach to interprocedurally inferring linear inequality relations. We propose an abstraction of the effects of procedures through convex sets of transition matrices. In the absence of conditional branching, this abstraction can be characterised precisely by means of the least solution of a constraint system. In order to handle conditionals, we introduce auxiliary variables and postpone checking them until after the procedure calls. In order to obtain an effective analysis, we approximate convex sets by means of polyhedra. Since our implementation of function composition uses the frame representation of polyhedra, we rely on the subclass of simplices to obtain an efficient implementation. We show that for this abstraction the basic operations can be implemented in polynomial time. First practical experiments indicate that the resulting analysis is quite efficient and provides reasonably precise results.