Paper Info
Title
An Abstract Interpretation Approach for Automatic Generation of Polynomial Invariants
Abstract
A method for generating polynomial invariants of imperative programs is presented using the abstract interpretation framework. It is shown that for programs with polynomial assignments, an invariant consisting of a conjunction of polynomial equalities can be automatically generated for each program point. The proposed approach takes into account tests in conditional statements as well as in loops, insofar as they can be abstracted to be polynomial equalities and disequalities. The semantics of each statement is given as a transformation on polynomial ideals. Merging of paths in a program is defined as the intersection of the polynomial ideals associated with each path. For a loop junction, a widening operator based on selecting polynomials up to a certain degree is proposed. The algorithm for finding invariants using this widening operator is shown to terminate in finitely many steps. The proposed approach has been implemented and successfully tried on many programs. A table providing details about the programs is given.
Year
DOI
Venue
2004
10.1007/978-3-540-27864-1_21
Lecture Notes in Computer Science
DocType
Volume
ISSN
Conference
3148
0302-9743
Citations 
PageRank 
References 
29
1.62
9
Authors
2
Name
Order
Citations
PageRank
Enric Rodríguez-Carbonell144626.13
Deepak Kapur22282235.00