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In this paper, we study LTLf synthesis under environment specifications forarbitrary reachability and safety properties. We consider both kinds ofproperties for both agent tasks and environment specifications, providing acomplete landscape of synthesis algorithms. For each case, we devise a specificalgorithm (optimal wrt complexity of the problem) and prove its correctness.The algorithms combine common building blocks in different ways. While somecases are already studied in literature others are studied here for the firsttime.

LTLf Synthesis Under Environment Specifications for Reachability and Safety Properties