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Parametric weighted finite automata (PWFA) are a multi-dimensional generalization of weighted finite automata. The expressiveness of PWFA contains the expressiveness of weighted finite automata as well as the expressiveness of affine iterated function system. The thesis discusses theory and applications of PWFA. The properties of PWFA definable sets are studied and it is shown that some fractal generator systems can be simulated using PWFA and that various real and complex functions can be represented by PWFA. Furthermore, the decoding of PWFA and the interpretation of PWFA definable sets is discussed.