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The paper discusses the merits of temporal testers, which can serve as a compositional basis for automata construction corresponding to temporal formulas in the context of ltl, psl, and mitllogics. Temporal testers can be viewed as (non-deterministic) transducers that, at any point, output a boolean value which is 1 iff the corresponding temporal formula holds starting at the current position.The main advantage of testers, compared to acceptors (such asBüchi automata) is their compositionality. Namely, a tester for a compound formula can be constructed out of the testers for its sub-formulas. Besides providing the construction of testers for formulas specified in ltl, psl, and mitl, the paper also presents a general overview of the tester methodology, and highlights some of the unique features and applications of transducers including compositional deductive verification of ltlproperties.