Tran, Dinh Duong and Ogata, Kazuhiro and Bui, Duy Dang and Gupta, Parth
(2020)
Lemma Weakening for State Machine Invariant Proofs.
In: THE 27TH ASIA-PACIFIC SOFTWARE ENGINEERING CONFERENCE.
Abstract
Lemma conjecture is one of the most challenging tasks in theorem proving. The paper focuses on invariant properties (or invariants) of state machines. Thus, lemmas are also invariants. To prove that a state predicate p is an invariant of a state machine M, in general, we need to find an inductive invariant q of M such that q(s) implies p(s) for all states s of M. q is often in the form p∧p', and p' is often in the form q1 ∧...∧qn. q1, ..., qn are the lemmas of the proof that p is an invariant of M. The paper proposes a technique called Lemma Weakening (LW). LW replaces qi with qi' such that qi(s) implies qi'(s) for all states s of M, which can make the proof reasonably tractable that may become otherwise unreasonably hard. MCS mutual exclusion protocol is used as an example to demonstrate the power of LW.
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