Symbolic optimization with SMT solvers

Yi, Li; Albarghouthi, Aws; Kincaid, Zachary; Gurfinkel, Arie; Chećhik, Marsha

doi:10.1145/2535838.2535857

Cited by 96 publications

(101 citation statements)

References 68 publications

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“…SMT has become a cornerstone in the programming languages and in the verification community, with contributions to program synthesis [41], constraint programming [54], and symbolic optimization [58]. The combination of SMT and equivalence relations has been the subject of recent investigations.…”

Section: Introductionmentioning

confidence: 99%

Symbolic computation of differential equivalences

Cardelli

Tribastone

Tschaikowski

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Ordinary differential equations (ODEs) are widespread in many natural sciences including chemistry, ecology, and systems biology, and in disciplines such as control theory and electrical engineering. Building on the celebrated molecules-as-processes paradigm, they have become increasingly popular in computer science, with highlevel languages and formal methods such as Petri nets, process algebra, and rule-based systems that are interpreted as ODEs.We consider the problem of comparing and minimizing ODEs automatically. Influenced by traditional approaches in the theory of programming, we propose differential equivalence relations. We study them for a basic intermediate language, for which we have decidability results, that can be targeted by a class of highlevel specifications. An ODE implicitly represents an uncountable state space, hence reasoning techniques cannot be borrowed from established domains such as probabilistic programs with finite-state Markov chain semantics. We provide novel symbolic procedures to check an equivalence and compute the largest one via partition refinement algorithms that use satisfiability modulo theories.We illustrate the generality of our framework by showing that differential equivalences include (i) well-known notions for the minimization of continuous-time Markov chains (lumpability), (ii) bisimulations for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics. With a prototype implementation we are able to detect equivalences in biochemical models from the literature that cannot be reduced using competing automatic techniques.

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Section: Introductionmentioning

confidence: 99%

Symbolic computation of differential equivalences

Cardelli

Tribastone

Tschaikowski

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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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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“…Similar approaches for template-based synthesis have been described, for instance, by Gawlitza and Seidl [2007], , and Li et al [2014]. However, these methods consider programs over mathematical integers.…”

Section: Reduction From Second-order To First-order Problemsmentioning

confidence: 97%

Bit-Precise Procedure-Modular Termination Analysis

Chen

David

Kroening

et al. 2017

ACM Trans. Program. Lang. Syst.

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Non-termination is the root cause of a variety of program bugs, such as hanging programs and denial-ofservice vulnerabilities. This makes an automated analysis that can prove the absence of such bugs highly desirable. To scale termination checks to large systems, an interprocedural termination analysis seems essential. This is a largely unexplored area of research in termination analysis, where most effort has focussed on small but difficult single-procedure problems.We present a modular termination analysis for C programs using template-based interprocedural summarisation. Our analysis combines a context-sensitive, over-approximating forward analysis with the inference of under-approximating preconditions for termination. Bit-precise termination arguments are synthesised over lexicographic linear ranking function templates. Our experimental results show the advantage of interprocedural reasoning over monolithic analysis in terms of efficiency, while retaining comparable precision.

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Symbolic optimization with SMT solvers

Cited by 96 publications

References 68 publications

Symbolic computation of differential equivalences

Symbolic computation of differential equivalences

Puli - A Problem-Specific OMT Solver

Bit-Precise Procedure-Modular Termination Analysis

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