SMT-RAT: An SMT-Compliant Nonlinear Real Arithmetic Toolbox

(Tool Presentation)
  • Florian Corzilius
  • Ulrich Loup
  • Sebastian Junges
  • Erika Ábrahám
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7317)


We present \(\texttt{SMT-RAT}\), a \(\texttt{C++}\) toolbox offering theory solver modules for the development of SMT solvers for nonlinear real arithmetic (NRA). NRA is an important but hard-to-solve theory and only fragments of it can be handled by some of the currently available SMT solvers. Our toolbox contains modules implementing the virtual substitution method, the cylindrical algebraic decomposition method, a Gröbner bases simplifier and a general simplifier. These modules can be combined according to a user-defined strategy in order to exploit their advantages.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ábrahám, E., et al.: A lazy SMT-solver for a non-linear subset of real algebra. In: Proc. of SMT 2010 (2010)Google Scholar
  2. 2.
    Basu, S., Pollack, R., Roy, M.: Algorithms in Real Algebraic Geometry. Springer (2010)Google Scholar
  3. 3.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (2009)Google Scholar
  4. 4.
    Brown, C.W.: QEPCAD B: A program for computing with semi-algebraic sets using CADs. SIGSAM Bulletin 37(4), 97–108 (2003)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bruttomesso, R., Pek, E., Sharygina, N., Tsitovich, A.: The OpenSMT Solver. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 150–153. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Collins, G.E.: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)Google Scholar
  7. 7.
    Corzilius, F., Ábrahám, E.: Virtual Substitution for SMT-Solving. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 360–371. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
  9. 9.
    de Moura, L., Passmore, G.O.: The strategy challenge in SMT solving,
  10. 10.
    Dolzmann, A., Sturm, T.: Simplification of quantifier-free formulas over ordered fields. Journal of Symbolic Computation 24, 209–231 (1995)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Dolzmann, A., Sturm, T.: REDLOG: Computer algebra meets computer logic. SIGSAM Bulletin 31(2), 2–9 (1997)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Fränzle, M., et al.: Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. Journal on Satisfiability, Boolean Modeling and Computation 1(3-4), 209–236 (2007)Google Scholar
  13. 13.
    Heintz, J., Roy, M.F., Solernó, P.: On the theoretical and practical complexity of the existential theory of the reals. The Computer Journal 36(5), 427–431 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Loup, U., Ábrahám, E.: GiNaCRA: A C++ Library for Real Algebraic Computations. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 512–517. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Passmore, G.O., Jackson, P.B.: Combined Decision Techniques for the Existential Theory of the Reals. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds.) MKM 2009, Held as Part of CICM 2009. LNCS, vol. 5625, pp. 122–137. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Tarski, A.: A Decision Method for Elementary Algebra and Geometry. University of California Press (1948)Google Scholar
  17. 17.
    Weispfenning, V.: A new approach to quantifier elimination for real algebra. In: Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation, pp. 376–392. Springer (1998)Google Scholar
  18. 18.
    Weispfenning, V.: The complexity of linear problems in fields. Journal of Symbolic Computation 5(1-2), 3–27 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Weispfenning, V.: Quantifier elimination for real algebra – The quadratic case and beyond. Applicable Algebra in Engineering, Communication and Computing 8(2), 85–101 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Florian Corzilius
    • 1
  • Ulrich Loup
    • 1
  • Sebastian Junges
    • 1
  • Erika Ábrahám
    • 1
  1. 1.RWTH Aachen UniversityGermany

Personalised recommendations