Computer Aided Verification

Volume 5123 of the series Lecture Notes in Computer Science pp 254-267

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

  • Himanshu JainAffiliated withSchool of Computer Science, Carnegie Mellon University
  • , Edmund ClarkeAffiliated withSchool of Computer Science, Carnegie Mellon University
  • , Orna GrumbergAffiliated withDepartment of Computer Science, Technion - Israel Institute of Technology

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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 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 counterexample guided abstraction refinement (CEGAR) framework. This has enabled verification of simple programs that cannot be checked using existing CEGAR based model checkers.