Being careful about theory combination

Dejan Jovanović, Clark Barrett

Research output: Contribution to journalArticlepeer-review


One of the main shortcomings of traditional methods for combining theories is the complexity of guessing the arrangement of variables shared by the individual theories. This paper presents a reformulation of the Nelson-Oppen method that takes into account explicit equality propagation and can ignore pairs of shared variables that the theories do not care about. We show the correctness of the new approach and present care functions for the theory of uninterpreted functions and the theory of arrays. The effectiveness of the new method is illustrated by experimental results demonstrating a dramatic performance improvement on benchmarks combining arrays and bit-vectors.

Original languageEnglish (US)
Pages (from-to)67-90
Number of pages24
JournalFormal Methods in System Design
Issue number1
StatePublished - Feb 2013


  • Nelson-Oppen
  • Satisfiability modulo theories
  • Theory combination

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture


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