Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations

Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations (2004)

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by Enric Rodríguez-carbonell , Deepak Kapur

Venue:	In International Symposium on Symbolic and Algebraic Computation 2004 (ISSAC04
Citations:	25 - 4 self

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Datum	Value	Source
TITLE	Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations	SVM HeaderParse 0.2
AUTHOR NAME	Enric Rodríguez-carbonell	SVM HeaderParse 0.2
AUTHOR AFFIL	LSI Department; Technical University of Catalonia	SVM HeaderParse 0.2
AUTHOR ADDR	Barcelona, Spain	SVM HeaderParse 0.2
AUTHOR NAME	Deepak Kapur	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of Computer Science; University of New Mexico	SVM HeaderParse 0.2
AUTHOR ADDR	Albuquerque, New Mexico, USA	SVM HeaderParse 0.2
ABSTRACT	This paper presents the algebraic foundation for an approach for generating polynomial loop invariants in imperative programs. It is first shown that the set of polynomials serving as loop invariants has the algebraic structure of an ideal. Using this connection, a procedure for finding loop invariants is given in terms of operations on ideals, for which Gröbner basis constructions can be employed. Most importantly, it is proved that if the assignment statements in a loop are solvable (in particular, affine) mappings with positive eigenvalues, then the procedure terminates in at most 2m + 1 iterations, where m is the number of variables in the loop. The proof is done by showing that the irreducible subvarieties of the variety associated with the polynomial ideal approximating the invariant polynomial ideal of the loop either stay the same or increase their dimension in every iteration. This yields a correct and complete algorithm for inferring conjunctions of polynomial equations as invariants. The method has been implemented in Maple using the Groebner package. The implementation has been used to automatically discover nontrivial invariants for several examples to illustrate the power of the techniques.	SVM HeaderParse 0.2
YEAR	2004	INFERENCE
VENUE	In International Symposium on Symbolic and Algebraic Computation 2004 (ISSAC04	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	266--273	INFERENCE
CITATIONS	20 found	ParsCit 1.0