Formal verification of crossover operator in Genetic Algorithms using Prototype Verification System (PVS)

Nawaz, M. Saqib; Lali, M. IkramUllah; Pasha, Muhammad Adeel

doi:10.1109/icet.2013.6743532

Cited by 8 publications

(3 citation statements)

References 7 publications

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“…The goal of Plaidypvs is to add to hybrid systems reasoning to the toolbox of PVS increasing its proving capabilities. PVS has been used in verification projects in domains such as aircraft avoidance systems [36], path planning algorithms [7], unmanned aircraft systems [34], position reporting algorithms of aircraft [13], sensor uncertainty mitigation [40], floating point error analysis [27,57], genetic algorithms [41], nonlinear control systems [3], and requirements written in linear temporal logic and FRETish [8]. In addition to advanced real number reasoning capabilities [9,35,38,28,37,39] provided by PVS, previous work has connected PVS to the automated theorem prover MetiTarski [2], for automated reasoning of universally quantified statements about real numbers, including several transcendental functions [11].…”

Section: Related Workmentioning

confidence: 99%

Embedding Differential Dynamic Logic in PVS

Slagel,

Moscato,

White

et al. 2024

Electron. Proc. Theor. Comput. Sci.

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Differential dynamic logic (dL) is a formal framework for specifying and reasoning about hybrid systems, i.e., dynamical systems that exhibit both continuous and discrete behaviors. These kinds of systems arise in many safety-and mission-critical applications. This paper presents a formalization of dL in the Prototype Verification System (PVS) that includes the semantics of hybrid programs and dL's proof calculus. The formalization embeds dL into the PVS logic, resulting in a version of dL whose proof calculus is not only formally verified, but is also available for the verification of hybrid programs within PVS itself. This embedding, called Plaidypvs (Properly Assured Implementation of dL for Hybrid Program Verification and Specification), supports standard dL style proofs, but further leverages the capabilities of PVS to allow reasoning about entire classes of hybrid programs. The embedding also allows the user to import the well-established definitions and mathematical theories available in PVS.

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Section: Related Workmentioning

confidence: 99%

Embedding Differential Dynamic Logic in PVS

Slagel,

Moscato,

White

et al. 2024

Electron. Proc. Theor. Comput. Sci.

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“…Function TAKE can cut the child list of list before the natural number, and function DROP can cut the child list of list after the natural number. In order to prove the properties of the formalized crossover operators, it is necessary to prove the properties of TAKE and DROP (Darmochwal and Nakamura, 1991 ; Kotowicz, 1993 ; Uchibori and Endou, 1999 ; Vidal et al, 2008 ; Nawaz et al, 2013 ). Since the existing properties of APPEND in HOL4 are sufficient, there is no need for more proofs.…”

Section: Higher-order Logic Representation Of Crossover Operators: Bamentioning

confidence: 99%

“…In Vidal et al ( 2008 ), a mathematical abstraction of crossover operators is proposed to extend the applicability of formalized crossover operators in genetic algorithms. In Nawaz et al ( 2013 ), the correctness of genetic algorithms with formalized crossover operators is verified. While the above studies lay the foundation for formalizing crossover operations of genetic algorithms, effective mechanisms and techniques are still urgently needed for developing correctness-guaranteed formalized crossover operations that can be easily deployed in genetic algorithms in practice.…”

Section: Introductionmentioning

confidence: 99%

Bio-Inspired Genetic Algorithms with Formalized Crossover Operators for Robotic Applications

Zhang

Kang

et al. 2017

Front. Neurorobot.

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Genetic algorithms are widely adopted to solve optimization problems in robotic applications. In such safety-critical systems, it is vitally important to formally prove the correctness when genetic algorithms are applied. This paper focuses on formal modeling of crossover operations that are one of most important operations in genetic algorithms. Specially, we for the first time formalize crossover operations with higher-order logic based on HOL4 that is easy to be deployed with its user-friendly programing environment. With correctness-guaranteed formalized crossover operations, we can safely apply them in robotic applications. We implement our technique to solve a path planning problem using a genetic algorithm with our formalized crossover operations, and the results show the effectiveness of our technique.

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