SMT-RAT  24.02
Toolbox for Strategic and Parallel Satisfiability-Modulo-Theories Solving
Bibliography
[1]

Cristina Borralleras, Salvador Lucas, Albert Oliveras, Enric Rodríguez-Carbonell, and Albert Rubio. Sat modulo linear arithmetic for solving polynomial constraints. Journal of Automated Reasoning, 48(1):107–131, Jan 2012.

[2]

Martin Bromberger and Christoph Weidenbach. Fast cube tests for lia constraint solving. In Nicola Olivetti and Ashish Tiwari, editors, Automated Reasoning, pages 116–132, Cham, 2016. Springer International Publishing.

[3]

Christopher W. Brown. Improved projection for cylindrical algebraic decomposition. Journal of Symbolic Computation, 32(5):447 – 465, 2001.

[4]

Alessandro Cimatti, Alberto Griggio, Ahmed Irfan, Marco Roveri, and Roberto Sebastiani. Satisfiability modulo transcendental functions via incremental linearization. In Leonardo de Moura, editor, Automated Deduction – CADE 26, pages 95–113, Cham, 2017. Springer International Publishing.

[5]

G. E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Automata Theory and Formal Languages, volume 33 of LNCS, pages 134–183. Springer, 1975.

[6]

F. Corzilius and E. Ábrahám. Virtual substitution for SMT solving. In 18th Int. Symp. on Fundamentals of Computation Theory, 2011.

[7]

Isil Dillig, Thomas Dillig, and Alex Aiken. Cuts from proofs: a complete and practical technique for solving linear inequalities over integers. Formal Methods in System Design, 39(3):246–260, 2011.

[8]

B. Dutertre and L. de Moura. A fast linear-arithmetic solver for DPLL(T). In Proc. of CAV'06, volume 4144 of LNCS, pages 81–94. Springer, 2006.

[9]

Pascal Fontaine, Mizuhito Ogawa, Thomas Sturm, and Xuan Tung Vu. Subtropical satisfiability. In International Symposium on Frontiers of Combining Systems, pages 189–206. Springer, 2017.

[10]

Carsten Fuhs, Jürgen Giesl, Aart Middeldorp, Peter Schneider-Kamp, René Thiemann, and Harald Zankl. Sat solving for termination analysis with polynomial interpretations. In João Marques-Silva and Karem A. Sakallah, editors, Theory and Applications of Satisfiability Testing – SAT 2007, pages 340–354, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg.

[11]

S. Gao, M. K. Ganai, F. Ivancic, A. Gupta, S. Sankaranarayanan, and E. M. Clarke. Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems. In Proc. of FMCAD'10, pages 81–89. IEEE, 2010.

[12]

Alberto Griggio. A practical approach to satisfiability modulo linear integer arithmetic. Journal on Satisfiability, Boolean Modeling and Computation, 8:1–27, 2012.

[13]

Marta Grobelna. Solving pseudo-boolean constraints, 2017.

[14]

Stefan Herbort and Dietmar Ratz. Improving the efficiency of a nonlinear-system-solver using a componentwise newton method. 1997.

[15]

H. Hong. An improvement of the projection operator in cylindrical algebraic decomposition. In Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC '90, pages 261–264, New York, NY, USA, 1990. ACM.

[16]

Ahmed Irfan. Incremental linearization for satisfiability and verification modulo nonlinear arithmetic and transcendental functions. PhD thesis, University of Trento, 2018.

[17]

S. Junges, U. Loup, F. Corzilius, and E. Ábrahám. On Gröbner bases in the context of satisfiability-modulo-theories solving over the real numbers. Technical Report AIB-2013-08, RWTH Aachen University, 2013.

[18]

Gereon Kremer and Erika Ábrahám. Fully incremental cylindrical algebraic decomposition. Journal of Symbolic Computation, 2019.

[19]

Gereon Kremer, Florian Corzilius, and Erika Ábrahám. A Generalised Branch-and-Bound Approach and Its Application in SAT Modulo Nonlinear Integer Arithmetic. In Proc. of CASC'16, pages 315–335. Springer, 2016.

[20]

Andreas Krüger. Bitvectors in smt-rat and their application to integer arithmetics, 2015.

[21]

Daniel Lazard. An Improved Projection for Cylindrical Algebraic Decomposition, chapter 29, pages 467–476. Springer, 1994.

[22]

U. Loup, K. Scheibler, F. Corzilius, Erika E. Ábrahám, and Bernd Becker. A symbiosis of interval constraint propagation and cylindrical algebraic decomposition. In Proc. of CADE-24, volume 7898 of LNCS, pages 193–207. Springer, 2013.

[23]

Scott McCallum. An improved projection operation for cylindrical algebraic decomposition, pages 277–278. Springer Berlin Heidelberg, Berlin, Heidelberg, 1985.

[24]

Robert Nieuwenhuis and Albert Oliveras. Fast congruence closure and extensions. Information and Computation, 205(4):557 – 580, 2007. Special Issue: 16th International Conference on Rewriting Techniques and Applications.

[25]

Aklima Zaman. Incremental linearization for sat modulo real arithmetic solving, 2019.

[26]

Ömer Sali. Linearization techniques for nonlinear arithmetic problems in smt, 2018.