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The fixed-point theory of strictly causal functions. (English) Zbl 1318.68116
Summary: 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 modeling 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, introduce a corresponding induction principle, and study the related convergence process.

MSC:
 68Q55 Semantics in the theory of computing 06B35 Continuous lattices and posets, applications 54H25 Fixed-point and coincidence theorems (topological aspects) 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
Software:
Esterel; SysML; SystemC
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