A Mixed Real and Floating-Point Solver

Salvia, Rocco; Titolo, Laura; Feliú, Marco A.; Moscato, Mariano M.; Muñoz, César; Rakamarić, Zvonimir

doi:10.1007/978-3-030-20652-9_25

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…Given the unstable conditions produced by PRECiSA for the winding number algorithm, an over-approximation of the region of instability is generated by using the paving functionality of the Kodiak global optimizer [26]. Concrete examples for these instability conditions are searched in the instability region by using the FPRoCK [29] solver, a tool able to check the satisfiability of mixed real and floating-point Boolean expressions. As an example, consider the edge (v, v ′ ), where v = (1, 1) and v ′ = (3, 2), in the polygon depicted in Fig.…”

Section: Test-stable Version Of the Winding Numbermentioning

confidence: 99%

Provably Correct Floating-Point Implementation of a Point-in-Polygon Algorithm

Moscato

Titolo

Feliú

et al. 2019

Lecture Notes in Computer Science

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The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floatingpoint implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-inpolygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a sourceto-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS).

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Section: Test-stable Version Of the Winding Numbermentioning

confidence: 99%

Provably Correct Floating-Point Implementation of a Point-in-Polygon Algorithm

Moscato

Titolo

Feliú

et al. 2019

Lecture Notes in Computer Science

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“…Many of these solvers implement very different algorithms to tackle the satisfiability problem for (a combination of) first-order theories, with significantly varying performance profiles. For example, in the quantifier-free theory of floating-point arithmetic (QF FP), there exist several substantially different decision procedures, e.g., bit-blasting [16], abstract CDCL [14], interreduction methods [55], and reduction to global optimization [22,11]. In this specific setting of floating-point solvers, input instances may be derived from a variety of applications, such as software verification or analysis of machine learning (ML) models [56].…”

Section: Introductionmentioning

confidence: 99%

MachSMT: A Machine Learning-based Algorithm Selector for SMT Solvers

Scott

Niemetz

Preiner

et al. 2021

Lecture Notes in Computer Science

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In this paper, we present MachSMT, an algorithm selection tool for Satisfiability Modulo Theories (SMT) solvers. MachSMT supports the entirety of the SMT-LIB language. It employs machine learning (ML) methods to construct both empirical hardness models (EHMs) and pairwise ranking comparators (PWCs) over state-of-the-art SMT solvers. Given an SMT formula $$\mathcal {I}$$ I as input, MachSMT leverages these learnt models to output a ranking of solvers based on predicted run time on the formula $$\mathcal {I}$$ I . We evaluate MachSMT on the solvers, benchmarks, and data obtained from SMT-COMP 2019 and 2020. We observe MachSMT frequently improves on competition winners, winning $$54$$ 54 divisions outright and up to a $$198.4$$ 198.4 % improvement in PAR-2 score, notably in logics that have broad applications (e.g., BV, LIA, NRA, etc.) in verification, program analysis, and software engineering. The MachSMT tool is designed to be easily tuned and extended to any suitable solver application by users. MachSMT is not a replacement for SMT solvers by any means. Instead, it is a tool that enables users to leverage the collective strength of the diverse set of algorithms implemented as part of these sophisticated solvers.

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Towards Numerical Assistants

Panchekha

Tatlock

2020

Lecture Notes in Computer Science

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A Mixed Real and Floating-Point Solver

Cited by 8 publications

References 16 publications

Provably Correct Floating-Point Implementation of a Point-in-Polygon Algorithm

Provably Correct Floating-Point Implementation of a Point-in-Polygon Algorithm

MachSMT: A Machine Learning-based Algorithm Selector for SMT Solvers

Towards Numerical Assistants

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