Formal Methods in System Design

, Volume 47, Issue 1, pp 1–25 | Cite as

On recursion-free Horn clauses and Craig interpolation

  • Philipp Rümmer
  • Hossein Hojjat
  • Viktor Kuncak


One of the main challenges in software verification is efficient and precise analysis of programs with procedures and loops. Interpolation methods remain among the most promising techniques for such verification. To accommodate the demands of various programming language features, over the past years several extended forms of interpolation have been introduced. We give a precise ontology of such extended interpolation methods, and investigate the relationship between interpolation and fragments of constrained recursion-free Horn clauses. We also introduce a new notion of interpolation, disjunctive interpolation, which solves a more general class of problems in one step compared to previous notions of interpolants, such as tree interpolants or inductive sequences of interpolants. We present algorithms and complexity for construction of interpolants, as well as the corresponding decision problems for recursion-free Horn fragments. Finally, we give an extensive empirical evaluation using a solver for (recursive) Horn problems, in particular comparing the performance of tree interpolation and disjunctive interpolation for constraints modelling software verification tasks.


Horn clause verification Interpolation Software verification SMT solver Software model checking Predicate abstraction 



We would like to thank Shaz Qadeer for discussions about the complexity of checking bounded recursive programs.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Philipp Rümmer
    • 1
  • Hossein Hojjat
    • 2
  • Viktor Kuncak
    • 3
  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden
  2. 2.Department of Computer ScienceCornell UniversityIthacaUSA
  3. 3.EPFL IC IIF LARALausanneSwitzerland

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