Programming: the derivation of algorithms
Programming: the derivation of algorithms
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
An axiomatic basis for computer programming
Communications of the ACM
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
Computing polynomial program invariants
Information Processing Letters
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 the algebraic relations of C-finite sequences and multisequences
Journal of Symbolic Computation
Aligator: A Mathematica Package for Invariant Generation (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Reasoning algebraically about P-solvable loops
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Inference of polynomial invariants for imperative programs: a farewell to gröbner bases
SAS'12 Proceedings of the 19th international conference on Static Analysis
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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We present an algorithm for generating all polynomial invariants of P-solvable loops with assignments and nested conditionals. We prove termination of our algorithm. The proof relies on showing that the dimensions of the prime ideals from the minimal decomposition of the ideals generated at an iteration of our algorithm either remain the same or decrease at the next iteration of the algorithm. Our experimental results report that our method takes less iterations and/or time than other polynomial invariant generation techniques.