  Monotonicity in concurrent systems stipulates that, in any global state,
extant system actions remain executable when new processes are added to the
state. This concept is not only natural and common in multi-threaded software,
but also useful: if every thread's memory is finite, monotonicity often
guarantees the decidability of safety property verification even when the
number of running threads is unknown. In this paper, we show that the act of
obtaining finite-data thread abstractions for model checking can be at odds
with monotonicity: Predicate-abstracting certain widely used monotone software
results in non-monotone multi-threaded Boolean programs - the monotonicity is
lost in the abstraction. As a result, well-established sound and complete
safety checking algorithms become inapplicable; in fact, safety checking turns
out to be undecidable for the obtained class of unbounded-thread Boolean
programs. We demonstrate how the abstract programs can be modified into
monotone ones, without affecting safety properties of the non-monotone
abstraction. This significantly improves earlier approaches of enforcing
monotonicity via overapproximations.
