A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
Automatic synthesis of optimal invariant assertions: Mathematical foundations
Proceedings of the 1977 symposium on Artificial intelligence and programming languages
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
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
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
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We discuss interesting properties of a general technique for inferring polynomial invariants for a subfamily of imperative loops, called the P-solvable loops, with assignments only. The approach combines algorithmic combinatorics, polynomial algebra and computational logic, and it is implemented in a new software package called Aligator.We present a collection of examples illustrating the power of the framework.