Puli - A Problem-Specific OMT Solver

Kovásznai, Gergely; Bíró, Csaba; Erdélyi, Balázs

doi:10.29007/96p4

Cited by 5 publications

(9 citation statements)

References 10 publications

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“…The aim of this paper is to improve our previous results on SMT-based optimization of WSNs. To do so, we apply SAT solvers parallel to SMT solvers, in a portfolio setting and hence improve our previous results [10] by a SAT/SMTbased portfolio approach for WSN optimization. Section II introduces basic concepts and definitions on SAT, SMT and OMT solving, as well as the WSN model we apply, including some reliability and security constraints over WSNs.…”

Section: Introductionmentioning

confidence: 92%

“…WSN optimization is a monotonic optimization problem [10] meaning that, as incrementing the value of T , all the resulting SAT/SMT instances are satisfiable until exceeding the optimum. That is, there exists no UNSAT instances below the optimum.…”

Section: Portfolio Solving For Wsn Optimizationmentioning

confidence: 99%

“…In previous experiments with OMT solvers [5], [6], [10], we observed that the bottleneck for underlying SMT solvers was typically to solve satisfiable instances. In our current experiments with underlying SAT solvers, we observed the opposite: the SAT-based approach is rather powerful on satisfiable instances and poor on unsatisfiable ones.…”

Section: A Portfolio Sat and Smt Solvingmentioning

confidence: 99%

“…A follow-up paper [6] investigates further aspects of WSNs that make the OMT solving process even more challenging, and the paper reports on experiments with the OMT solvers OPTIMATHSAT [7], Z3 [8], and SYMBA [9]. In [10], we introduce our OMT solver called PULI and report on further experiments, showing that PULI significantly outperforms the aforementioned OMT solvers on WSN benchmarks. PULI uses the SMT solver Z3 [11] as underlying solver and calls Z3 iteratively.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Portfolio SAT and SMT Solving of Cardinality Constraints in Sensor Network Optimization

Kovásznai

Gajdar

Kovács

2019

2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

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Wireless Sensor Networks (WSNs) serve as the basis for Internet of Things applications. A WSN consists of a number of spatially distributed sensor nodes, which cooperatively monitor physical or environmental conditions. In order to ensure the dependability of WSN functionalities, several reliability and security requirements have to be fulfilled. In previous work, we applied OMT (Optimization Modulo Theories) solvers to maximize a WSN's lifetime, i.e., to generate an optimal sleep/wake-up scheduling for the sensor nodes. We discovered that the bottleneck for the underlying SMT (Satisfiability Modulo Theories) solvers was typically to solve satisfiable instances. In this paper, we encode the WSN verification problem as a set of Boolean cardinality constraints, therefore SAT solvers can also be applied as underlying solvers. We have experimented with different SAT solvers and also with different SAT encodings of Boolean cardinality constraints. Based on our experiments, the SAT-based approach is very powerful on satisfiable instances, but quite poor on unsatisfiable ones. In this paper, we apply both SAT and SMT solvers in a portfolio setting. Based on our experiments, the MiniCARD+Z3 setting can be considered to be the most powerful one, which outperforms OMT solvers by 1-2 orders of magnitude.

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Section: Introductionmentioning

confidence: 92%

Section: Portfolio Solving For Wsn Optimizationmentioning

confidence: 99%

Section: A Portfolio Sat and Smt Solvingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Portfolio SAT and SMT Solving of Cardinality Constraints in Sensor Network Optimization

Kovásznai

Gajdar

Kovács

2019

2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

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“…Optimization modulo theories (OMT) [6][7][8][9][20][21][22][23][28][29][30][31][32]35,36,[38][39][40][41][42][43] is an important extension to satisfiability modulo theories which allows for finding models that optimize one or more objectives, which typically consist in some linear-arithmetic or Pseudo-Boolean function application.…”

Section: Introductionmentioning

confidence: 99%

Optimization Modulo the Theories of Signed Bit-Vectors and Floating-Point Numbers

Trentin

Sebastiani

2021

J Autom Reasoning

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Optimization modulo theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or Pseudo-Boolean terms. However, many SMT and OMT applications, in particular from SW and HW verification, require handling bit-precise representations of numbers, which in SMT are handled by means of the theory of bit-vectors ($${{\mathcal {B}}}{{\mathcal {V}}}$$ B V ) for the integers and that of floating-point numbers ($$\mathcal {FP}$$ FP ) for the reals respectively. Whereas an approach for OMT with (unsigned) $${{\mathcal {B}}}{{\mathcal {V}}}$$ B V objectives has been proposed by Nadel & Ryvchin, unfortunately we are not aware of any existing approach for OMT with $$\mathcal {FP}$$ FP objectives. In this paper we fill this gap, and we address for the first time $$\text {OMT}$$ OMT with $$\mathcal {FP}$$ FP objectives. We present a novel OMT approach, based on the novel concept of attractor and dynamic attractor, which extends the work of Nadel and Ryvchin to work with signed-$${{\mathcal {B}}}{{\mathcal {V}}}$$ B V objectives and, most importantly, with $$\mathcal {FP}$$ FP objectives. We have implemented some novel $$\text {OMT}$$ OMT procedures on top of OptiMathSAT and tested them on modified problems from the SMT-LIB repository. The empirical results support the validity and feasibility of our novel approach.

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Generalized Optimization Modulo Theories

Tsiskaridze,

Barrett,

Tinelli

2024

Lecture Notes in Computer Science

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Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be optimal with respect to a given objective function. We introduce a generalization of the OMT problem where, in particular, objective functions can range over partially ordered sets. We provide a formalization of and an abstract calculus for the Generalized OMT problem and prove their key correctness properties. Generalized OMT extends previous work on OMT in several ways. First, in contrast to many current OMT solvers, our calculus is theory-agnostic, enabling the optimization of queries over any theories or combinations thereof. Second, our formalization unifies both single- and multi-objective optimization problems, allowing us to study them both in a single framework and facilitating the use of objective functions that are not supported by existing OMT approaches. Finally, our calculus is sufficiently general to fully capture a wide variety of current OMT approaches (each of which can be realized as a specific strategy for rule application in the calculus) and to support the exploration of new search strategies. Much like the original abstract DPLL(T) calculus for SMT, our Generalized OMT calculus is designed to establish a theoretical foundation for understanding and research and to serve as a framework for studying variations of and extensions to existing OMT methodologies.

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Puli - A Problem-Specific OMT Solver

Cited by 5 publications

References 10 publications

Portfolio SAT and SMT Solving of Cardinality Constraints in Sensor Network Optimization

Portfolio SAT and SMT Solving of Cardinality Constraints in Sensor Network Optimization

Optimization Modulo the Theories of Signed Bit-Vectors and Floating-Point Numbers

Generalized Optimization Modulo Theories

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