Automatic generation of invariants and intermediate assertions
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Global Data Flow Analysis and Iterative Algorithms
Journal of the ACM (JACM)
Symbolic evaluation and the global value graph
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Flow Analysis of Computer Programs
Flow Analysis of Computer Programs
Discovering affine equalities using random interpretation
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Polynomial Constants Are Decidable
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Powerful Techniques for the Automatic Generation of Invariants
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Computing polynomial program invariants
Information Processing Letters
Precise interprocedural analysis using random interpretation
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Analysis of modular arithmetic
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
A generic framework for interprocedural analysis of numerical properties
SAS'05 Proceedings of the 12th international conference on Static Analysis
Analysing All Polynomial Equations in ${\mathbb Z_{2^w}}$
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Invariant Checking for Programs with Procedure Calls
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Computing procedure summaries for interprocedural analysis
ESOP'07 Proceedings of the 16th European conference on Programming
Reasoning algebraically about P-solvable loops
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
ABC: algebraic bound computation for loops
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Inference of polynomial invariants for imperative programs: a farewell to gröbner bases
SAS'12 Proceedings of the 19th international conference on Static Analysis
ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
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Since programming languages are Turing complete, it is impossible to decide for all programs whether a given non-trivial semantic property is valid or not. The way-out chosen by abstract interpretation is to provide approximate methods which may fail to certify a program property on some programs. Precision of the analysis can be measured by providing classes of programs for which the analysis is complete, i.e., decides the property in question. Here, we consider analyses of polynomial identities between integer variables such as x1 . x2−2x3=0. We describe current approaches and clarify their completeness properties. We also present an extension of our approach based on weakest precondition computations to programs with procedures and equality guards.