On Using Floating-Point Computations to Help an Exact Linear Arithmetic Decision Procedure
نویسنده
چکیده
We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver and a simplex-based decision procedure for conjunctions. State-of-the-art SMT solvers use simplex implementations over rational numbers, which perform well for typical problems arising from model-checking and program analysis (sparse inequalities, small coefficients) but are slow for other applications (denser problems, larger
منابع مشابه
Dynamical Control of Computations Using the Family of Optimal Two-point Methods to Solve Nonlinear Equations
One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...
متن کاملA Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range
A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double format) and fast floating point operations as well as exact dot product computations. Due to floating point limitations it is not an arbitrary precision arithmetic. However, it typically allows computations using several hundre...
متن کاملAn Exact Rational Mixed-Integer Programming Solver
We present an exact rational solver for mixed-integer linear programming which avoids the numerical inaccuracies inherent in the floating-point computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbol...
متن کاملA hybrid branch-and-bound approach for exact rational mixed-integer programming
We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric imple...
متن کاملOn using an inexact floating-point LP solver for deciding linear arithmetic in an SMT solver
Off-the-shelf linear programming (LP) solvers trade soundness for speed: for efficiency, the arithmetic is not exact rational arithmetic but floating-point arithmetic. As a side-effect the results come without any formal guarantee and cannot be directly used for deciding linear arithmetic. In this work we explain how to design a sound procedure for linear arithmetic built upon an inexact floati...
متن کامل