Accession Number : ADA476796


Title :   Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations


Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE


Personal Author(s) : Jain, Himanshu ; Clarke, Edmund M ; Grumberg, Orna


Full Text : http://www.dtic.mil/dtic/tr/fulltext/u2/a476796.pdf


Report Date : Feb 2008


Pagination or Media Count : 40


Abstract : The use of Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms for obtaining proofs of unsatisfiability and interpolants for conjunctions of linear diophantine equations linear modular equations (linear congruences), and linear diophantine disequations. We show the utility of the proposed interpolation algorithms for discovering modular/divisibility predicates in a counter-example guided abstraction refinement (CEGAR) framework. This has enabled verification of simple programs that cannot be checked using existing CEGAR based model checkers.


Descriptors :   *INTERPOLATION , ALGORITHMS , MODULAR CONSTRUCTION , ARITHMETIC , LINEAR DIFFERENTIAL EQUATIONS , LINEAR ALGEBRAIC EQUATIONS , INTEGRAL EQUATIONS , POLYNOMIALS


Subject Categories : Numerical Mathematics
      Computer Systems


Distribution Statement : APPROVED FOR PUBLIC RELEASE