  We consider the synthesis of distributed implementations for specifications
in Prompt Linear Temporal Logic (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 systems, we show that, despite being more powerful, the
distributed realizability problem for PROMPT-LTL is not harder than its LTL
counterpart. For asynchronous systems we have to consider an assume-guarantee
synthesis problem, as we have to express scheduling assumptions. 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.
