Abstract
This paper connects research in computer science in the field of SAT-modulo-theories (SMT) solving and research in mathematics on decision procedures for real algebra. We consider a real algebraic decision procedure computing all realizable sign conditions of a set of polynomials. We modify this procedure so that it satisfies certain requirements needed for the embedding into an SMT-solver.
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Barrett, C., Sebastiani, R., Seshia, S., Tinelli, C.: Satisfiability Modulo Theories, ch. 26. Frontiers in Artificial Intelligence and Applications [5], vol. 185, pp. 825–885 (2009)
Barrett, C., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298–302. Springer, Heidelberg (2007)
Basu, S., Pollack, R., Roy, M.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2010)
Bauer, A., Pister, M., Tautschnig, M.: Tool-support for the analysis of hybrid systems and models. In: DATE 2007, pp. 924–929. European Design and Automation Association (2007)
Biere, A., Heule, M., van Maaren, H., Walsh, T.: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)
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)
Bruttomesso, R., Cimatti, A., Franzén, A., Griggio, A., Sebastiani, R.: The mathSAT 4SMT solver. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 299–303. Springer, Heidelberg (2008)
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)
Dutertre, B., Moura, L.D.: A fast linear-arithmetic solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)
Fränzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: 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)
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)
Marques-Silva, J., Lynce, I., Malik, S.: Conflict-Driven Clause Learning SAT Solvers, ch. 4. Frontiers in Artificial Intelligence and Applications [5], vol. 85, pp. 131–153 (2009)
Mishra, B.: Algorithmic Algebra. Texts and Monographs in Computer Science. Springer, Heidelberg (1993)
de Moura, L., Bjørner, N.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(T). Journal of the ACM 53, 937–977 (2006)
SMT competition 2010, http://www.smtcomp.org/2010/
Weispfenning, V.: Quantifier elimination for real algebra – The quadratic case and beyond. Applicable Algebra in Engineering, Communication and Computing 8(2), 85–101 (1997)
Zankl, H., Middeldorp, A.: Satisfiability of non-linear (Ir)rational arithmetic. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 481–500. Springer, Heidelberg (2010)
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Loup, U., Ábrahám, E. (2011). I-RiSC: An SMT-Compliant Solver for the Existential Fragment of Real Algebra. In: Winkler, F. (eds) Algebraic Informatics. CAI 2011. Lecture Notes in Computer Science, vol 6742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21493-6_15
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DOI: https://doi.org/10.1007/978-3-642-21493-6_15
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