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2018 | OriginalPaper | Buchkapitel

Polynomial Constraints and Unsat Cores in Tarski

verfasst von : Fernando Vale-Enriquez, Christopher W. Brown

Erschienen in: Mathematical Software – ICMS 2018

Verlag: Springer International Publishing

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Abstract

This paper gives a brief overview of Tarski, a system for computing with Tarski formulas, which are boolean combinations of non-linear polynomial constraints over the reals. It gives an overview of Tarski’s basic functionality, then goes into more detail on facilities Tarski provides for checking the satisfiability of conjunctions of constraints that are able to produce “unsat cores” for unsatisfiable inputs.

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Fußnoten
1
Tarski is available at https://​www.​usna.​edu/​Users/​cs/​wcbrown/​tarski/​. It is open source, distributed under an ISC-style license.
 
Literatur
1.
Zurück zum Zitat Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB standard: version 2.0. In: Gupta, A., Kroening, D. (eds.) Proceedings of the 8th International Workshop on Satisfiability Modulo Theories, Edinburgh, UK (2010) Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB standard: version 2.0. In: Gupta, A., Kroening, D. (eds.) Proceedings of the 8th International Workshop on Satisfiability Modulo Theories, Edinburgh, UK (2010)
2.
Zurück zum Zitat Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. ACM SIGSAM Bull. 37(4), 97–108 (2003)CrossRef Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. ACM SIGSAM Bull. 37(4), 97–108 (2003)CrossRef
3.
Zurück zum Zitat Brown, C.W.: Fast simplifications for Tarski formulas. In: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009, New York, NY, USA, pp. 63–70. ACM (2009) Brown, C.W.: Fast simplifications for Tarski formulas. In: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009, New York, NY, USA, pp. 63–70. ACM (2009)
4.
Zurück zum Zitat Brown, C.W.: Fast simplifications for Tarski formulas based on monomial inequalities. J. Symb. Comput. 47(7), 859–882 (2012)MathSciNetCrossRef Brown, C.W.: Fast simplifications for Tarski formulas based on monomial inequalities. J. Symb. Comput. 47(7), 859–882 (2012)MathSciNetCrossRef
5.
Zurück zum Zitat Brown, C.W., Davenport, J.H.: The complexity of quantifier elimination and cylindrical algebraic decomposition. In: Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, ISSAC 2007, New York, NY, USA, pp. 54–60. ACM (2007) Brown, C.W., Davenport, J.H.: The complexity of quantifier elimination and cylindrical algebraic decomposition. In: Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, ISSAC 2007, New York, NY, USA, pp. 54–60. ACM (2007)
6.
Zurück zum Zitat Brown, C.W., Strzeboński, A.: Black-box/white-box simplification and applications to quantifier elimination. In: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010, New York, NY, USA, pp. 69–76. ACM (2010) Brown, C.W., Strzeboński, A.: Black-box/white-box simplification and applications to quantifier elimination. In: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010, New York, NY, USA, pp. 69–76. ACM (2010)
8.
Zurück zum Zitat Chen, C., Davenport, J.H., Lemaire, F., Maza, M.M., Xia, B., Xiao, R., Xie, Y.: Computing the real solutions of polynomial systems with the RegularChains library in Maple. ACM Commun. Comput. Algebra 45, 166–168 (2011)CrossRef Chen, C., Davenport, J.H., Lemaire, F., Maza, M.M., Xia, B., Xiao, R., Xie, Y.: Computing the real solutions of polynomial systems with the RegularChains library in Maple. ACM Commun. Comput. Algebra 45, 166–168 (2011)CrossRef
10.
Zurück zum Zitat Davenport, J.H., Heintz, J.: Real quantifier elimination is doubly exponential. J. Symb. Comput. 5, 29–35 (1997)MathSciNetCrossRef Davenport, J.H., Heintz, J.: Real quantifier elimination is doubly exponential. J. Symb. Comput. 5, 29–35 (1997)MathSciNetCrossRef
11.
Zurück zum Zitat Dolzmann, A., Seidl, A., Sturm, T.: Efficient projection orders for CAD. In: Gutierrez, J. (ed.) Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation (ISSAC 2004), Santander, Spain, July 2004. ACM (2004) Dolzmann, A., Seidl, A., Sturm, T.: Efficient projection orders for CAD. In: Gutierrez, J. (ed.) Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation (ISSAC 2004), Santander, Spain, July 2004. ACM (2004)
13.
Zurück zum Zitat England, M., et al.: Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS (LNAI), vol. 8543, pp. 45–60. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08434-3_5CrossRef England, M., et al.: Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS (LNAI), vol. 8543, pp. 45–60. Springer, Cham (2014). https://​doi.​org/​10.​1007/​978-3-319-08434-3_​5CrossRef
14.
Zurück zum Zitat Huang, Z., England, M., Davenport, J.M., Paulson, L.C.: Using machine learning to decide when to precondition cylindrical algebraic decomposition with Groebner bases. In: 2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 45–52, September 2016 Huang, Z., England, M., Davenport, J.M., Paulson, L.C.: Using machine learning to decide when to precondition cylindrical algebraic decomposition with Groebner bases. In: 2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 45–52, September 2016
16.
Zurück zum Zitat McCallum, S.: Solving polynomial strict inequalities using cylindrical algebraic decomposition. Comput. J. 36(5), 432–438 (1993)MathSciNetCrossRef McCallum, S.: Solving polynomial strict inequalities using cylindrical algebraic decomposition. Comput. J. 36(5), 432–438 (1993)MathSciNetCrossRef
17.
Zurück zum Zitat Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: from an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53, 2006 (2006)MathSciNetCrossRef Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: from an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53, 2006 (2006)MathSciNetCrossRef
19.
20.
Zurück zum Zitat Tarski, A.: A Decision Method for Elementary Algebra and Geometry, Second edn. University of California Press, Berkeley (1951). rev. Reprinted in [7] Tarski, A.: A Decision Method for Elementary Algebra and Geometry, Second edn. University of California Press, Berkeley (1951). rev. Reprinted in [7]
21.
Metadaten
Titel
Polynomial Constraints and Unsat Cores in Tarski
verfasst von
Fernando Vale-Enriquez
Christopher W. Brown
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-96418-8_55

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