Abstract
Weighted finite automata (WFA) are nondeterministic finite automata labeled with real weights on their edges and states. They compute real functions on the unit interval. Parametric weighted finite automata (PWFA) are weighted finite automata with a multi-dimensional codomain. The only completely smooth functions computable by WFA are polynomials, while PWFA are also able to compute the sine, cosine, exponential and logarithmic function. We will present methods for constructing PWFA computing basic shapes, Catmull-Rom splines, Bezier polynomials and B-splines. We show how these possibilities can be combined to obtain a figure drawing framework that is based on a very simple automaton model that has only the operations of sum, multiplication by a constant and iteration.
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Tischler, G.: Properties and applications of parametric weighted finite automata submitted
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Tischler, G. (2005). Parametric Weighted Finite Automata for Figure Drawing. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_24
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DOI: https://doi.org/10.1007/978-3-540-30500-2_24
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