Endomorphisms for Non-trivial Non-linear Loop Invariant Generation

Authors:
Rachid Rebiha;Nadir Matringe;Arnaldo Vieira Moura
Affiliations:
Faculty of Informatics, University of Lugano, Switzerland and Institute of Computing, University of Campinas, Brasil;Institue de Mathematiques de Jussieu (UMR 7586), Université Paris, France;Institute of Computing, University of Campinas, Brasil
Venue:
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Year:
2008

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Abstract

Present approaches for non-linear loop invariant generation are limited to linear (affine) systems, or they relay on non scalable methods which have high complexity. Moreover, for programs with nested loops and conditional statements that describe multivariate polynomials or multivariate fractional systems, no applicable method is known to lend itself to non-trivialnon-linear invariants generation. We demonstrate a powerful computational completemethod to solve this problem. Our approach avoids first-order quantifier elimination, cylindrical algebraic decomposition and Grobner bases computation, hereby circumventing difficulties met by recent methods.