Data-Driven Template-Free Invariant Generation
CoRR(2023)
摘要
Automatic verification of concurrent programs faces state explosion due to
the exponential possible interleavings of its sequential components coupled
with large or infinite state spaces. An alternative is deductive verification,
where given a candidate invariant, we establish inductive invariance and show
that any state satisfying the invariant is also safe. However, learning
(inductive) program invariants is difficult. To this end, we propose a
data-driven procedure to synthesize program invariants, where it is assumed
that the program invariant is an expression that characterizes a (hopefully
tight) over-approximation of the reachable program states. The main ideas of
our approach are: (1) We treat a candidate invariant as a classifier separating
states observed in (sampled) program traces from those speculated to be
unreachable. (2) We develop an enumerative, template-free approach to learn
such classifiers from positive and negative examples. At its core, our
enumerative approach employs decision trees to generate expressions that do not
over-fit to the observed states (and thus generalize). (3) We employ a runtime
framework to monitor program executions that may refute the candidate
invariant; every refutation triggers a revision of the candidate invariant. Our
runtime framework can be viewed as an instance of statistical model checking,
which gives us probabilistic guarantees on the candidate invariant. We also
show that such in some cases, our counterexample-guided inductive synthesis
approach converges (in probability) to an overapproximation of the reachable
set of states. Our experimental results show that our framework excels in
learning useful invariants using only a fraction of the set of reachable states
for a wide variety of concurrent programs.
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