Synthesis for Prefix First-Order Logic on Data Words

We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as first-order logic formulas from a fragment we call prefix first-order logic that implements a limited kind of order. We show that this logic has nice properties that enable us to prove decidability of the synthesis problem.