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
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A Technique for Invariant Generation
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
A Transformational Approach for Generating Non-linear Invariants
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Delay Analysis in Synchronous Programs
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
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
Algebraic Power Analysis by Abstract Interpretation
Higher-Order and Symbolic Computation
Precise widening operators for convex polyhedra
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Precise widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Modeling, optimization and computation for software verification
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Theoretical Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
A data driven approach for algebraic loop invariants
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
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A technique for generating invariant polynomial inequalities of bounded degree is presented using the abstract interpretation framework. It is based on overapproximating basic semi-algebraic sets, i.e., sets defined by conjunctions of polynomial inequalities, by means of convex polyhedra. While improving on the existing methods for generating invariant polynomial equalities, since polynomial inequalities are allowed in the guards of the transition system, the approach does not suffer from the prohibitive complexity of the methods based on quantifier-elimination. The application of our implementation to benchmark programs shows that the method produces non-trivial invariants in reasonable time. In some cases the generated invariants are essential to verify safety properties that cannot be proved with classical linear invariants.