  We look at nondeterministic finite automata augmented with multiple
reversal-bounded counters where, during an accepting computation, the behavior
of the counters is specified by some fixed pattern. These patterns can serve as
a useful "bridge" to other important automata and grammar models in the
theoretical computer science literature, thereby helping in their study.
Various pattern behaviors are considered, together with characterizations and
comparisons. For example, one such pattern defines exactly the smallest full
trio containing all the bounded semilinear languages. Another pattern defines
the smallest full trio containing all the bounded context-free languages. The
"bridging" to other families is then applied, e.g. to certain Turing machine
restrictions, as well as other families. Certain general decidability
properties are also studied using this framework.
