No, AWS does not use any publicly available cloud solutions. OpenStack is an open source platform for creating and maintaining the cloud Infrastructure as a Service. It mostly is directly for the private cloud market, where companies or individual users who needs complete control on how their infrastructure is provisioned can use the platform and create their own cloud. AWS is a public cloud provider and uses their own custom solution to do the same and hence they don't use any code from OpenStack and their code base is a closed source.
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