OptiMathSAT: A Tool for Optimization Modulo Theories

Sebastiani, Roberto; Trentin, Patrick

doi:10.1007/978-3-319-21690-4_27

Cited by 89 publications

(108 citation statements)

References 14 publications

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“…In those experiments, we compare the results by OptiMathSAT [13], Z3 [3], and Symba [12]. We conclude there that OptiMathSAT provides the most stable performance and scales the best.…”

Section: Introductionmentioning

confidence: 90%

Puli - A Problem-Specific OMT Solver

Kovásznai¹,

Bíró²,

Erdélyi³

2018

EasyChair Preprints

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In our previous papers, we investigated several aspects of applying Optimization Modulo Theories (OMT) solvers to Wireless Sensor Networks (WSNs). None of the solvers we used in our experiments scaled enough for WSNs of common size in practice. This is particularly true when investigating additional dependability and security constraints on WSNs of high density.In this paper, we propose an idea of speeding up the OMT solving process by taking into consideration some resources in the systems and by applying regression analysis on those resource values. For instance, in WSNs, the electrical charge in the batteries of sensor nodes can be considered to be a resource that is being consumed as approaching the maximal lifetime of the network. Another example is the knapsack problem where the remaining capacity of the knapsack can be used as such a resource. We show how to integrate this idea in search algorithms in the OMT framework and introduce a new OMT solver called Puli. We present experiments with Puli on WSN and knapsack benchmarks, which show remarkable improvements in the number of solved instances as well as computation time compared to existing solvers. Furthermore, we show that further signicant improvement can be realized on so-called monotonous problems, such as WSN optimization, for which Puli can generate more precise assertions. We present Puli as a work-in-progress prototype that we are planning to upgrade to an ocial release soon, which we want to make publicly available.

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“…In those experiments, we compare the results by OptiMathSAT [13], Z3 [3], and Symba [12]. We conclude there that OptiMathSAT provides the most stable performance and scales the best.…”

Section: Introductionmentioning

confidence: 90%

Puli - A Problem-Specific OMT Solver

Kovásznai¹,

Bíró²,

Erdélyi³

2018

EasyChair Preprints

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“…The resulting Max-SMT formula can be processed with an off-the-shelf Max-SMT solver, such as Opti-Mathsat [32], Z3Opt [33] or Barcelogic [34]. Unfortunately, we had to discard Opti-Mathsat because it cannot deal with nonlinearities.…”

Section: Methodsmentioning

confidence: 99%

Speeding up the Constraint-Based Method in Difference Logic

Candeago

Larraz

Oliveras

et al. 2016

Theory and Applications of Satisfiability Testing – SAT 2016

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Abstract. Over the years the constraint-based method has been successfully applied to a wide range of problems in program analysis, from invariant generation to termination and non-termination proving. Quite often the semantics of the program under study as well as the properties to be generated belong to difference logic, i.e., the fragment of linear arithmetic where atoms are inequalities of the form u − v ≤ k. However, so far constraint-based techniques have not exploited this fact: in general, Farkas' Lemma is used to produce the constraints over template unknowns, which leads to non-linear SMT problems. Based on classical results of graph theory, in this paper we propose new encodings for generating these constraints when program semantics and templates belong to difference logic. Thanks to this approach, instead of a heavyweight non-linear arithmetic solver, a much cheaper SMT solver for difference logic or linear integer arithmetic can be employed for solving the resulting constraints. We present encouraging experimental results that show the high impact of the proposed techniques on the performance of the VeryMax verification system.

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“…The latest version of dReal [21] now implements Optimization Modulo Theory (OMT) [29,7]. OMT is an extension of SMT which allows for finding models that optimize given objectives.…”

Section: The Dreal Solvermentioning

confidence: 99%

Robustness of Neural Networks to Parameter Quantization

Murthy¹,

Das

Islam

2019

From Reactive Systems to Cyber-Physical Systems

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Keywords: Neural Networks · Edge Computing · Parameter Quantization · Robustness · Satisfiability Modulo Theories Quantization, a commonly used technique to reduce the memory footprint of a neural network for edge computing, entails reducing the precision of the floating-point representation used for the parameters of the network. The impact of such rounding-off errors on the overall performance of the neural network is estimated using testing, which is not exhaustive and thus cannot be used to guarantee the safety of the model. We present a framework based on Satisfiability Modulo Theory (SMT) solvers to quantify the robustness of neural networks to parameter perturbation. To this end, we introduce notions of local and global robustness that capture the deviation in the confidence of class assignments due to parameter quantization. The robustness notions are then cast as instances of SMT problems and solved automatically using solvers, such as dReal. We demonstrate our framework on two simple Multi-Layer Perceptrons (MLP) that perform binary classification on a two-dimensional input. In addition to quantifying the robustness, we also show that Rectified Linear Unit activation results in higher robustness than linear activations for our MLPs.

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OptiMathSAT: A Tool for Optimization Modulo Theories

Cited by 89 publications

References 14 publications

Puli - A Problem-Specific OMT Solver

Puli - A Problem-Specific OMT Solver

Speeding up the Constraint-Based Method in Difference Logic

Robustness of Neural Networks to Parameter Quantization

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