Theory of linear and integer programming
Theory of linear and integer programming
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
A new lower bound construction for commutative thue systems with applications
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Communications of the ACM
The new math of computer programming
Communications of the ACM
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
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A Discipline of Programming
Principles of Program Analysis
Principles of Program Analysis
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Automatic synthesis of optimal invariant assertions: Mathematical foundations
Proceedings of the 1977 symposium on Artificial intelligence and programming languages
Mathematical Theory of Computation
Mathematical Theory of Computation
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
A synthesizer of inductive assertions
IEEE Transactions on Software Engineering
Property extraction in well-founded property sets
IEEE Transactions on Software Engineering
Analysing All Polynomial Equations in ${\mathbb Z_{2^w}}$
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
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We present a static analysis that approximates the relational semantics of imperative programs by systems of low-degree polynomial equalities. Our method is based on Abstract Interpretation in a lattice of polynomial pseudo ideals - finite-dimensional vector spaces of degree-bounded polynomials that are closed under degree-bounded products. For a fixed degree bound, the sizes of bases of pseudo ideals and the lengths of chains in the lattice of pseudo ideals are bounded by polynomials in the number of program variables. Despite the approximate nature of our analysis, for several programs taken from the literature on non-linear polynomial invariant generation our method produces results that are as precise as those produced by methods based on polynomial ideals and Grobner bases.