Efficient solving of quantified inequality constraints over the real numbers

Ratschan, Stefan

doi:10.1145/1166109.1166113

Cited by 41 publications

(77 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has been work on QCSP with continuous domains, using one or more UQV and dedicated algorithms [2,5,15]. Discrete QCSP algorithms cannot be used to reason about uncertain data since they apply a preprocessing step enforced by the solver QCSPsolve [10], which essentially determines whether constraints of the form ∀X, ∀Y, C(X, Y ), and ∃Z, ∀Y, C(Z, Y ), are either always true or false for all values of a UQV.…”

Section: Related Workmentioning

confidence: 99%

Uncertain Data Dependency Constraints in Matrix Models

Gervet¹,

Galichet²

2015

Integration of AI and OR Techniques in Constraint Programming

View full text Add to dashboard Cite

Abstract. Uncertain data due to imprecise measurements is commonly specified as bounded intervals in a constraint decision or optimization problem. Dependencies do exist among such data, e.g. upper bound on the sum of uncertain production rates per machine, sum of traffic distribution ratios from a router over several links. For tractability reasons existing approaches in constraint programming or robust optimization frameworks assume independence of the data. This assumption is safe, but can lead to large solution spaces, and a loss of problem structure. Thus it cannot be overlooked. In this paper we identify the context of matrix models and show how data dependency constraints over the columns of such matrices can be modeled and handled efficiently in relationship with the decision variables. Matrix models are linear models whereby the matrix cells specify for instance, the duration of production per item, the production rates, or the wage costs, in applications such as production planning, economics, inventory management. Data imprecision applies to the cells of the matrix and the output vector. Our approach contributes the following results: 1) the identification of the context of matrix models with data constraints, 2) an efficient modeling approach of such constraints that suits solvers from multiple paradigms. An illustration of the approach and its benefits are shown on a production planning problem.

show abstract

Section: Related Workmentioning

confidence: 99%

Uncertain Data Dependency Constraints in Matrix Models

Gervet¹,

Galichet²

2015

Integration of AI and OR Techniques in Constraint Programming

View full text Add to dashboard Cite

show abstract

“…Solving the constraints Different approaches exist to handle the quantified constraints (4a)-(4c). A branch-and-prune approach is presented in [19]. It performs branching over constraints and eliminates all irrelevant points.…”

Section: B Interval Formulationmentioning

confidence: 99%

Computation of parametric barrier functions for dynamical systems using interval analysis

Bouissou

Chapoutot

Djaballah

et al. 2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-The formal verification of safety properties for hybrid systems is an important but challenging problem. Recently, barrier functions have been introduced to prove safety without requiring the computation of the reachable set of continuous or hybrid dynamical systems.This paper presents a new approach for the construction of barrier functions for safety verification of nonlinear dynamical systems. The proposed method is based on the search for the parameters of a parametric barrier function using interval analysis. This technique allows considering complex dynamics without needing any relaxation of constraints in the barrier function.

show abstract

“…RSolver [2] is a numerical approach for deciding validity of (robust instances of) first-order formulas over real arithmetic extended with transcendental functions. Unlike our work, this relies on numerical stability of the input formula.…”

Section: Related Workmentioning

confidence: 99%

“…However, for a large number of real-world systems, the underlying problems in real arithmetic still have a prohibitive complexity for quantifier elimination. Even numerical procedures for real arithmetic [2] suffer from the curse of dimensionality limiting their scalability.…”

Section: Introductionmentioning

confidence: 99%

Real World Verification

Platzer

Quesel

Rümmer

2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Scalable handling of real arithmetic is a crucial part of the verification of hybrid systems, mathematical algorithms, and mixed analog/digital circuits. Despite substantial advances in verification technology, complexity issues with classical decision procedures are still a major obstacle for formal verification of real-world applications, e.g., in automotive and avionic industries. To identify strengths and weaknesses, we examine state of the art symbolic techniques and implementations for the universal fragment of real-closed fields: approaches based on quantifier elimination, Gröbner Bases, and semidefinite programming for the Positivstellensatz. Within a uniform context of the verification tool KeYmaera, we compare these approaches qualitatively and quantitatively on verification benchmarks from hybrid systems, textbook algorithms, and on geometric problems. Finally, we introduce a new decision procedure combining Gröbner Bases and semidefinite programming for the real Nullstellensatz that outperforms the individual approaches on an interesting set of problems.

show abstract

Efficient solving of quantified inequality constraints over the real numbers

Cited by 41 publications

References 49 publications

Uncertain Data Dependency Constraints in Matrix Models

Uncertain Data Dependency Constraints in Matrix Models

Computation of parametric barrier functions for dynamical systems using interval analysis

Real World Verification

Contact Info

Product

Resources

About