Crowdsourcing consists in hiring workers on internet to perform large amounts of simple, independent and replicated work units, before assembling the returned results. A challenge to solve intricate problems is to define orchestrations of tasks, and allow higher-order answers where workers can suggest a process to obtain data rather than a plain answer. Another challenge is to guarantee that an orchestration with correct input data terminates, and produces correct output data. This work proposes complex workflows, a data-centric model for crowdsourcing based on orchestration of concurrent tasks and higher order schemes. We consider termination (whether some/all runs of a complex workflow terminate) and correctness (whether some/all runs of a workflow terminate with data satisfying FO requirements). We show that existential termination/correctness are undecidable in general excepted for specifications with bounded recursion. However, universal termination/correctness are decidable when constraints on inputs are specified in a decidable fragment of FO, and are at least in co - 2EXPTIME.
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