  The notion of delays arises naturally in many computational models, such as,
in the design of circuits, control systems, and dataflow languages. In this
work, we introduce \emph{automata with delay blocks} (ADBs), extending finite
state automata with variable time delay blocks, for deferring individual
transition output symbols, in a discrete-time setting. We show that the ADB
languages strictly subsume the regular languages, and are incomparable in
expressive power to the context-free languages. We show that ADBs are closed
under union, concatenation and Kleene star, and under intersection with regular
languages, but not closed under complementation and intersection with other ADB
languages. We show that the emptiness and the membership problems are decidable
in polynomial time for ADBs, whereas the universality problem is undecidable.
Finally we consider the linear-time model checking problem, i.e., whether the
language of an ADB is contained in a regular language, and show that the model
checking problem is PSPACE-complete.
