Solving non-linear arithmetic

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7364 LNAI, Issue , 2012, Pages 339-354

  Jovanović, Dejan ^a   De Moura, Leonardo ^b  

^a NEW YORK UNIVERSITY   (United States)

^b MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARITHMETIC CONSTRAINTS; CLAUSE LEARNING; CYLINDRICAL ALGEBRAIC DECOMPOSITIONS; PROJECTION OPERATOR; SATISFIABILITY;

ALGORITHMS;

CONSTRAINT THEORY;

EID: 84863632916     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-31365-3_27     Document Type: Conference Paper

References (29)

1. Akbarpour, B., Paulson, L.C.: MetiTarski: An automatic theorem prover for real-valued special functions. Journal of Automated Reasoning 44(3), 175-205 (2010)
2. Barrett, C., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298-302. Springer, Heidelberg (2007)
3. Basu, S., Pollack, R., Roy, M.-F.: Algorithms in real algebraic geometry. Springer (2006)
4. Brown, C.W.: Solution formula construction for truth invariant CAD's. PhD thesis, University of Delaware (1999)
5. Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. ACM SIGSAM Bulletin 37(4), 97-108 (2003)
6. Brown, W.S., Traub, J.F.: On Euclid's algorithm and the theory of subresultants. Journal of the ACM 18(4), 505-514 (1971)
7. Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds.): Computer algebra. Symbolic and algebraic computation. Springer (1982)
8. Caviness, B.F., Johnson, J.R. (eds.): Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation. Springer (2004)
9. Cohen, H.: A Course in Computational Algebraic Number Theory. Springer (1993)
10. 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)
11. de Moura, L., Bjørner, N.S.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337-340. Springer, Heidelberg (2008)
12. Dolzmann, A., Sturm, T.: Redlog: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31(2), 2-9 (1997)
13. 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)
14. Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H.: SAT Solving for Termination Analysis with Polynomial Interpretations. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 340-354. Springer, Heidelberg (2007)
15. Hong, H.: Comparison of several decision algorithms for the existential theory of the reals (1991)
16. Jovanović, D., de Moura, L.: Cutting to the Chase Solving Linear Integer Arithmetic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 338-353. Springer, Heidelberg (2011)
17. Korovin, K., Tsiskaridze, N., Voronkov, A.: Conflict Resolution. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 509-523. Springer, Heidelberg (2009)
18. Loos, R.: Generalized polynomial remainder sequences. Computer Algebra: Symbolic and Algebraic Computation, 115-137 (1982)
19. McLaughlin, S., Harrison, J.V.: A Proof-Producing Decision Procedure for Real Arithmetic. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 295-314. Springer, Heidelberg (2005)
20. McMillan, K.L., Kuehlmann, A., Sagiv, M.: Generalizing DPLL to Richer Logics. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 462-476. Springer, Heidelberg (2009)
21. 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(6), 937-977 (2006)
22. Passmore, G.O.: Combined Decision Procedures for Nonlinear Arithmetics, Real and Complex. PhD thesis, University of Edinburgh (2011)
23. Platzer, A., Quesel, J.-D., Rümmer, P.: Real World Verification. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 485-501. Springer, Heidelberg (2009)
24. Silva, J.P.M., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48(5), 506-521 (1999)
25. Strzeboński, A.W.: Cylindrical algebraic decomposition using validated numerics. Journal of Symbolic Computation 41(9), 1021-1038 (2006)
26. Tarski, A.: A decision method for elementary algebra and geometry. Technical Report R-109, Rand Corporation (1951)
27. Tiwari, A.: An Algebraic Approach for the Unsatisfiability of Nonlinear Constraints. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 248-262. Springer, Heidelberg (2005)
28. Weispfenning, V.: Quantifier elimination for real algebra - the quadratic case and beyond. AAECC 8, 85-101 (1993)
29. 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)