Countable nondeterminism and random assignment
Journal of the ACM (JACM)
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Automatic generation of invariants and intermediate assertions
Theoretical Computer Science - Special issue: principles and practice of constraint programming
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
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 invariants of bounded degree using abstract interpretation
Science of Computer Programming
Generating all polynomial invariants in simple loops
Journal of Symbolic Computation
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Analysing All Polynomial Equations in ${\mathbb Z_{2^w}}$
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Finding positively invariant sets of a class of nonlinear loops via curve fitting
Proceedings of the 2009 conference on Symbolic numeric computation
Invariant generation for P-solvable loops with assignments
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Polynomial invariants for linear loops
Cybernetics and Systems Analysis
Journal of Symbolic Computation
SIAM Journal on Control and Optimization
An iterative method for generating loop invariants
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Invariant and type inference for matrices
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Checking herbrand equalities and beyond
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
On the computational complexity of dynamic slicing problems for program schemas
Mathematical Structures in Computer Science - Programming Language Interference and Dependence
Analysis of modular arithmetic
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Derivation of non-structural invariants of petri nets using abstract interpretation
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
A complete invariant generation approach for p-solvable loops
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Acceleration of the abstract fixpoint computation in numerical program analysis
Journal of Symbolic Computation
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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
A data driven approach for algebraic loop invariants
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
| Hi-index | 0.89 |
We present two automatic program analyses. The first analysis checks if a given polynomial relation holds among the program variables whenever control reaches a given program point. It fully interprets assignment statements with polynomial expressions on the right-hand side and polynomial disequality guards. Other assignments are treated as non-deterministically assigning any value and guards that are not polynomial disequalities are ignored. The second analysis extends this checking procedure. It computes the set of all polynomial relations of an arbitrary given form that are valid at a given target program point. It is also complete up to the abstraction described above.