  We consider the synthesis of distributed implementations for specifications
in parameterized temporal logics such as PROMPT-LTL, which extends LTL by
temporal operators equipped with parameters that bound their scope. For single
process synthesis it is well-established that such parametric extensions do not
increase worst-case complexities. For synchronous distributed systems we show
that, despite being more powerful, the realizability problem for PROMPT-LTL is
not harder than its LTL counterpart. For asynchronous systems we have to
express scheduling assumptions and therefore consider an assume-guarantee
synthesis problem. As asynchronous distributed synthesis is already undecidable
for LTL, we give a semi-decision procedure for the PROMPT-LTL assume-guarantee
synthesis problem based on bounded synthesis. Finally, we show that our results
extend to the stronger logics PLTL and PLDL.
