Programming from specifications
Programming from specifications
An axiomatic basis for computer programming
Communications of the ACM
The Science of Programming
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
A Discipline of Programming
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An Algorithm for Automated Generation of Invariants for Loops with Conditionals
SYNASC '05 Proceedings of the Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Variance analyses from invariance analyses
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Daikon system for dynamic detection of likely invariants
Science of Computer Programming
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
HASE '08 Proceedings of the 2008 11th IEEE High Assurance Systems Engineering Symposium
Mathematics for reasoning about loop functions
Science of Computer Programming
Finding Loop Invariants for Programs over Arrays Using a Theorem Prover
SYNASC '09 Proceedings of the 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Reflexive transitive invariant relations: A basis for computing loop functions
Journal of Symbolic Computation
Program verification using automatic generation of invariants
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Using invariant relations in the termination analysis of while loops
Proceedings of the 34th International Conference on Software Engineering
Invariant functions and invariant relations: An alternative to invariant assertions
Journal of Symbolic Computation
Verifying while loops with invariant relations
International Journal of Critical Computer-Based Systems
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Since their introduction more than four decades ago, invariant assertions have, justifiably, dominated the analysis of while loops, and have been the focus of sustained research interest in the seventies and eighties, and renewed interest in the last decade. In this paper, we tentatively submit an alternative concept for the analysis of while loops, explore its attributes, its applications, and its relationship to invariant assertions. Also, we discuss the design, implementation and use of a tool that analyzes while loops using this concept.