Programming: the derivation of algorithms
Programming: the derivation of algorithms
On the mechanical derivation of loop invariants
Journal of Symbolic Computation - Special issue on automatic 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
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A Discipline of Programming
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Non-linear loop invariant generation using Gröbner bases
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
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
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
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Harnessing a Refinement Theory to Compute Loop Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Mathematics for reasoning about loop functions
Science of Computer Programming
Relational Methods in the Analysis of While Loops: Observations of Versatility
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Verification by parallelization of parametric code
Algebraic and proof-theoretic aspects of non-classical logics
Reflexive transitive invariant relations: A basis for computing loop functions
Journal of Symbolic Computation
Invariant relations: an automated tool to analyze loops
VECoS'11 Proceedings of the Fifth international conference on Verification and Evaluation of Computer and Communication Systems
JSART: javascript assertion-based regression testing
ICWE'12 Proceedings of the 12th international conference on Web Engineering
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Invariant functions and invariant relations: An alternative to invariant assertions
Journal of Symbolic Computation
Invariant relations, invariant functions, and loop functions
Innovations in Systems and Software Engineering
Verifying while loops with invariant relations
International Journal of Critical Computer-Based Systems
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In an earlier paper, an algorithm based on algebraic geometry was developed for discovering polynomial invariants in loops without nesting, not requiring any a priori bound on the degree of the invariants. Polynomial invariants were shown to form an ideal, a basis of which could be computed using Gröbner bases methods. In this paper, an abstract logical framework is presented for automating the discovery of invariants for loops without nesting, of which the algorithm based on algebraic geometry and Gröbner bases is one particular instance. The approach based on this logical abstract framework is proved to be correct and complete. The techniques have been used with a verifier to automatically check properties of many non-trivial programs with considerable success. Some of these programs are discussed in the paper to illustrate the effectiveness of the method.