  By algorithmic metatheorems for a model checking problem P over
infinite-state systems we mean generic results that can be used to infer
decidability (possibly complexity) of P not only over a specific class of
infinite systems, but over a large family of classes of infinite systems. Such
results normally start with a powerful formalism of infinite-state systems,
over which P is undecidable, and assert decidability when is restricted by
means of an extra "semantic condition" C. We prove various algorithmic
metatheorems for the problems of model checking LTL and its two common
fragments LTL(Fs,Gs) and LTLdet over the expressive class of word/tree
automatic transition systems, which are generated by synchronized finite-state
transducers operating on finite words and trees. We present numerous
applications, where we derive (in a unified manner) many known and previously
unknown decidability and complexity results of model checking LTL and its
fragments over specific classes of infinite-state systems including pushdown
systems; prefix-recognizable systems; reversal-bounded counter systems with
discrete clocks and a free counter; concurrent pushdown systems with a bounded
number of context-switches; various subclasses of Petri nets; weakly extended
PA-processes; and weakly extended ground-tree rewrite systems. In all cases,we
are able to derive optimal (or near optimal) complexity. Finally, we pinpoint
the exact locations in the arithmetic and analytic hierarchies of the problem
of checking a relevant semantic condition and the LTL model checking problems
over all word/tree automatic systems.
