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Mechanical Verification of Automatic Synthesis of Fault-Tolerant Programs

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International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR)
Fault-tolerance is a crucial property in many systems. Thus, mechanical verification of algorithms associated with synthesis of fault-tolerant programs is desirable to ensure their correctness. In this paper, we present the mechanized verification of algorithms that automate the addition of fault-tolerance to a given fault-intolerant program using the PVS theorem prover. By this verification, not only we prove the correctness of the synthesis algorithms, but also we guarantee that any program synthesized by these algorithms is correct by construction. Towards this end, we formally define a uniform framework for formal specification and verification of fault-tolerance that consists of abstract definitions for programs, specifications, faults, and levels of fault-tolerance, so that they are independent of platform and architecture. The essence of synthesis algorithms involves fixpoint calculations. Hence, we also develop a reusable library for fixpoint calculations on finite sets in PVS.