A timed model for communicating sequential processes
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Topology, computer science, and the mathematics of convergence
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Strictly causal functions have a unique fixed point
Theoretical Computer Science
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Generalized metrics and uniquely determined logic programs
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CPO semantics of timed interactive actor networks
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive fixed-point theorem for these functions, and introduce a corresponding induction principle.