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## A Fast Linear-Arithmetic Solver for DPLL(T) (2006)

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Citations: | 282 - 13 self |

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1890 |
Theory of Linear and Integer Programming
- Schrijver
- 1986
(Show Context)
Citation Context ... to integer variables. To be complete in the integer or mixed integer case, we employ a branch and cut strategy, that is, the combination of branch-and-bound with a cutting plane generation algorithm =-=[17,18]-=-. The branch-and-bound algorithm works when problems are solved in Qδ rather than Q. In other words, it can be used when strict inequalities are present. The cutting-plane method we use is based on mi... |

1365 |
Integer and Combinatorial Optimization
- Nemhauser, Wolsey
- 1988
(Show Context)
Citation Context ... to integer variables. To be complete in the integer or mixed integer case, we employ a branch and cut strategy, that is, the combination of branch-and-bound with a cutting plane generation algorithm =-=[17,18]-=-. The branch-and-bound algorithm works when problems are solved in Qδ rather than Q. In other words, it can be used when strict inequalities are present. The cutting-plane method we use is based on mi... |

427 | Simplify: a theorem prover for program checking
- Detlefs, Nelson, et al.
(Show Context)
Citation Context ...kin elimination explodes on many problems and Simplex is generally superior. The common methods for integrating a Simplex solver with DPLL rely on incremental versions of Simplex such as described in =-=[11,12,13,14]-=-. A tableau is constructed and updated incrementally: rows are added as DPLL proceeds and are later removed when DPLL backtracks. These frequent addition and removal of rows and the related bookkeepin... |

232 |
CVC Lite: A new implementation of the cooperating validity checker
- Barrett, Berezin
- 2004
(Show Context)
Citation Context ...lized for the difference-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used by CVClite =-=[4]-=-, CVC [5], SVC [6]) or on Simplex methods [7] (used by MathSat [8], ICS [9], Simplics, Yices, ARIO [10]). Fourier-Motzkin elimination explodes on many problems and Simplex is generally superior. The c... |

161 | Validity Checking for Combinations of Theories with Equality
- Barrett, Dill, et al.
- 1996
(Show Context)
Citation Context ...erence-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used by CVClite [4], CVC [5], SVC =-=[6]-=-) or on Simplex methods [7] (used by MathSat [8], ICS [9], Simplics, Yices, ARIO [10]). Fourier-Motzkin elimination explodes on many problems and Simplex is generally superior. The common methods for ... |

150 | Compiling with proofs
- NECULA
- 1998
(Show Context)
Citation Context ...kin elimination explodes on many problems and Simplex is generally superior. The common methods for integrating a Simplex solver with DPLL rely on incremental versions of Simplex such as described in =-=[11,12,13,14]-=-. A tableau is constructed and updated incrementally: rows are added as DPLL proceeds and are later removed when DPLL backtracks. These frequent addition and removal of rows and the related bookkeepin... |

142 | DPLL( T): Fast Decision Procedures
- Ganzinger, Hagen, et al.
- 2004
(Show Context)
Citation Context ...ee linear arithmetic determine whether a boolean combination of linear equalities, inequalities, and disequalities is satisfiable. Several tools for solving this problem rely on the DPLL(T ) approach =-=[1]-=-: they combine boolean satisfiability solvers based on the Davis-Putnam-Logemann-Loveland (DPLL) procedure, and arithmetic solvers capable of deciding the satisfiability of conjunctions of linear cons... |

138 |
Fourier-motzkin elimination and its dual
- Dantzig, Eaves
- 1973
(Show Context)
Citation Context ...lice [20]) are specialized for the difference-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination =-=[3]-=- (used by CVClite [4], CVC [5], SVC [6]) or on Simplex methods [7] (used by MathSat [8], ICS [9], Simplics, Yices, ARIO [10]). Fourier-Motzkin elimination explodes on many problems and Simplex is gene... |

126 |
The Satisfiability Modulo Theories Library (SMT-LIB), www.SMT-LIB.org
- Ranise, Tinelli
- 2006
(Show Context)
Citation Context ... and their predecessor ICS, which does not. – Theory propagation is useful if it can be done cheaply. Figure 1 compares the results of Simplics on the real-arithmetic subset of the SMT-LIB benchmarks =-=[15]-=- using different levels of theory propagation. By default, Simplics uses a heuristic form of propagation that is relatively inexpensive but incomplete (no pivoting is used). This is compared in Figure... |

121 | CVC: A Cooperating Validity Checker
- Stump, Barrett, et al.
- 2002
(Show Context)
Citation Context ... the difference-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used by CVClite [4], CVC =-=[5]-=-, SVC [6]) or on Simplex methods [7] (used by MathSat [8], ICS [9], Simplics, Yices, ARIO [10]). Fourier-Motzkin elimination explodes on many problems and Simplex is generally superior. The common met... |

115 | The cassowary linear arithmetic constraint solving algorithm
- Badros, Borning, et al.
- 2001
(Show Context)
Citation Context ...kin elimination explodes on many problems and Simplex is generally superior. The common methods for integrating a Simplex solver with DPLL rely on incremental versions of Simplex such as described in =-=[11,12,13,14]-=-. A tableau is constructed and updated incrementally: rows are added as DPLL proceeds and are later removed when DPLL backtracks. These frequent addition and removal of rows and the related bookkeepin... |

51 | DPLL(T) with exhaustive theory propagation and its application to dierence logic
- Nieuwenhuis, Oliveras
- 2005
(Show Context)
Citation Context ...ity of conjunctions of linear constraints. Results of a first satisfiability modulo theories (SMT) competition, comparing several of these tools, are presented in [2]. Several tools (e.g., Barcelogic =-=[21]-=- or Slice [20]) are specialized for the difference-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimina... |

38 | Efficient satisfiability modulo theories via delayed theory combination
- Bozzano, Bruttomesso, et al.
- 2005
(Show Context)
Citation Context ...rent theories. In most cases, the number of such shared variables is small in comparison with the total number of variables and this method is quite efficient. This approach is described in detail at =-=[19]-=-. It can be extended with an opportunistic equality-propagation method [16]. 7 Experiments Figure 6 compares a prototype SMT solver that uses the previous algorithms with other tools that participated... |

24 | Integrating simplex with DPLL(T
- Dutertre, Moura
- 2006
(Show Context)
Citation Context ...by removing any variable xi that does not occur in any elementary atom of Φ ′ . This is done by Gaussian elimination. In practice, this presimplification can reduce the matrix size significantly (cf. =-=[16]-=-). The variables si introduced during the transformation play the same role as the slack variables of standard Simplex. However, the presence of both lower and upper bounds is beneficial. For example,... |

17 | The mathsat 3 system
- Bozzano, Bruttomesso, et al.
- 2005
(Show Context)
Citation Context ...ely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used by CVClite [4], CVC [5], SVC [6]) or on Simplex methods [7] (used by MathSat =-=[8]-=-, ICS [9], Simplics, Yices, ARIO [10]). Fourier-Motzkin elimination explodes on many problems and Simplex is generally superior. The common methods for integrating a Simplex solver with DPLL rely on i... |

16 | Solving linear arithmetic constraints
- Rueß, Shankar
- 2004
(Show Context)
Citation Context |

14 | Design and Results of the 1st Satisfiability Modulo Theories Competition (SMT-COMP 2005
- Barrett, Moura, et al.
(Show Context)
Citation Context ...s capable of deciding the satisfiability of conjunctions of linear constraints. Results of a first satisfiability modulo theories (SMT) competition, comparing several of these tools, are presented in =-=[2]-=-. Several tools (e.g., Barcelogic [21] or Slice [20]) are specialized for the difference-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools... |

13 |
ICS: Integrated Canonization and Solving
- Filliâtre, Owre, et al.
- 2001
(Show Context)
Citation Context ...aph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used by CVClite [4], CVC [5], SVC [6]) or on Simplex methods [7] (used by MathSat [8], ICS =-=[9]-=-, Simplics, Yices, ARIO [10]). Fourier-Motzkin elimination explodes on many problems and Simplex is generally superior. The common methods for integrating a Simplex solver with DPLL rely on incrementa... |

12 | A Scalable Method for Solving Satisfiability of Integer Linear Arithmetic Logic
- Sheini, Sakallah
- 2005
(Show Context)
Citation Context ... linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used by CVClite [4], CVC [5], SVC [6]) or on Simplex methods [7] (used by MathSat [8], ICS [9], Simplics, Yices, ARIO =-=[10]-=-). Fourier-Motzkin elimination explodes on many problems and Simplex is generally superior. The common methods for integrating a Simplex solver with DPLL rely on incremental versions of Simplex such a... |

4 |
Deciding Separation Logic Formulae with SAT by Incremental Negative Cycle Elimination
- Wang, Ivancic, et al.
- 2005
(Show Context)
Citation Context ...tions of linear constraints. Results of a first satisfiability modulo theories (SMT) competition, comparing several of these tools, are presented in [2]. Several tools (e.g., Barcelogic [21] or Slice =-=[20]-=-) are specialized for the difference-logic fragment of linear arithmetic and rely on graph algorithms. For general linear arithmetic, existing tools rely either on FourierMotzkin elimination [3] (used... |