  We study monitoring of linear-time arithmetic properties against finite
traces generated by an unknown dynamic system. The monitoring state is
determined by considering at once the trace prefix seen so far, and all its
possible finite-length, future continuations. This makes monitoring at least as
hard as satisfiability and validity. Traces consist of finite sequences of
assignments of a fixed set of variables to numerical values. Properties are
specified in a logic we call ALTLf, combining LTLf (LTL on finite traces) with
linear arithmetic constraints that may carry lookahead, i.e., variables may be
compared over multiple instants of the trace. While the monitoring problem for
this setting is undecidable in general, we show decidability for (a) properties
without lookahead, and (b) properties with lookahead that satisfy the abstract,
semantic condition of finite summary, studied before in the context of model
checking. We then single out concrete, practically relevant classes of
constraints guaranteeing finite summary. Feasibility is witnessed by a
prototype implementation.
