Trancón y Widemann, B; Hauhs, M: Algebrais-Coalgebraic recursion theory of histroy-dependent dynamical system models in Bonsangue, M.M.: Coalgebraic Methods in Computer Science, Springer, 225-244 (2014), doi:10.007/978-3-662-44124-4_13
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.

Keywords: Recursion theory, Dynamical systems, State-based models, History-dependent models

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