Algebraic–Coalgebraic Recursion Theory of History-Dependent Dynamical System Models

Abstract : We investigate the common recursive structure of history-dependent dynamic models in science and engineering. We give formal semantics in terms of a hybrid algebraic–coalgebraic scheme, namely course-of-value iteration. This theoretical approach yields categories of observationally equivalent model representations with precise semantic relationships. Along the initial–final axis of these categories, history dependence can appear both literally and transformed into instantaneous state. The framework can be connected to philosophical and epistemological discourse on one side, and to algorithmic considerations for computational modeling on the other.
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Baltasar Trancón y Widemann, Michael Hauhs. Algebraic–Coalgebraic Recursion Theory of History-Dependent Dynamical System Models. 12th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2014, Grenoble, France. pp.225-244, ⟨10.1007/978-3-662-44124-4_13⟩. ⟨hal-01408762⟩

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