Lemma Weakening for State Machine Invariant Proofs

• Published in: 2020 27th Asia-Pacific Software Engineering Conference (APSEC) pp. 21 - 30
• Main Authors: Tran, Duong Dinh, Bui, Dang Duy, Gupta, Parth, Ogata, Kazuhiro
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2020
• Subjects: algebraic specification language; Knowledge engineering; lemma conjecture; lemma strengthening; lemma weakening; MCS protocol; proof score; Protocols; Software engineering; Systematics; Task analysis
• ISSN: 2640-0715
• DOI: 10.1109/APSEC51365.2020.00010

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\wedge p^{\prime} , and p^{\prime} is often in the form q_{1}\wedge\ldots\wedge q_{n}.\ q_{1}, \ldots, q_{n} are the lemmas of the proof that p is an invariant of M . The paper proposes a technique called Lemma Weakening (LW). LW replaces q_{i} with q^{\prime}_{i} such that q_{i}(s) implies q_{i}^{\prime}(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.