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<TITLE>Priority Inversion Protocol</TITLE>
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<H2>Proving the Priority Inheritance Protocol Correct</H2>
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By Xingyuan Zhang, Christian Urban and Chunhan Wu
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<p>
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In real-time systems with threads, resource locking and
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priority scheduling, one faces the problem of Priority
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Inversion. This problem can make the behaviour of threads
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unpredictable and the resulting bugs can be hard to find. The
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Priority Inheritance Protocol is one solution implemented in many
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systems for solving this problem, but the correctness of this solution
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has never been formally verified in a theorem prover. As already
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pointed out in the literature, the original informal investigation of
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the Property Inheritance Protocol presents a correctness "proof" for
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an incorrect algorithm. In this paper we fix the problem of
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this proof by making all notions precise and implementing a variant of
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a solution proposed earlier. Our formalisation in Isabelle/HOL
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uncovers facts not mentioned in the literature, but also shows how to
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efficiently implement this protocol. Earlier correct implementations
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were criticised as too inefficient. Our formalisation is based on
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Paulson's inductive approach to verifying protocols.
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