Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems

Authors:
Sicun Gao;Malay Ganai;Franjo Ivančić;Aarti Gupta;Sriram Sankaranarayanan;Edmund M. Clarke
Affiliations:
NEC Labs America, NJ and Carnegie Mellon University, PA;NEC Labs America, NJ;NEC Labs America, NJ;NEC Labs America, NJ;University of Colorado, Boulder, CO;Carnegie Mellon University, PA
Venue:
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Year:
2010

Citing 10
Cited 7

Solving Polynomial Systems Using a Branch and Prune Approach

SIAM Journal on Numerical Analysis
Quantified constraints under perturbation

Journal of Symbolic Computation
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques

ACM Transactions on Mathematical Software (TOMS)
The complexity of quantifier elimination and cylindrical algebraic decomposition

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Decision Procedures: An Algorithmic Point of View

Decision Procedures: An Algorithmic Point of View
Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Real World Verification

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
An analysis of slow convergence in interval propagation

CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Localization of an underwater robot using interval constraint propagation

CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
A fast linear-arithmetic solver for DPLL(T)

CAV'06 Proceedings of the 18th international conference on Computer Aided Verification

Integration of an LP solver into interval constraint propagation

COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Superposition modulo non-linear arithmetic

FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
δ-complete decision procedures for satisfiability over the reals

IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Delta-Decidability over the Reals

LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Abstract partial cylindrical algebraic decomposition i: the lifting phase

CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
dReal: an SMT solver for nonlinear theories over the reals

CADE'13 Proceedings of the 24th international conference on Automated Deduction
Sound compilation of reals

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a novel integration of interval constraint propagation (ICP) with SMT solvers for linear real arithmetic (LRA) to decide nonlinear real arithmetic problems. We use ICP to search for interval solutions of the nonlinear constraints, and use the LRA solver to either validate the solutions or provide constraints to incrementally refine the search space for ICP. This serves the goal of separating the linear and nonlinear solving stages, and we show that the proposed methods preserve the correctness guarantees of ICP. Experimental results show that such separation is useful for enhancing efficiency.