Rational series and their languages
Rational series and their languages
Finite Automata Computing Real Functions
SIAM Journal on Computing
Image-data compression using edge-optimizing algorithm for WFA inference
Information Processing and Management: an International Journal - Special issue: data compression
On computational power of weighted finite automata
Fundamenta Informaticae - Special issue on formal language theory
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
On generalizations of weighted finite automata and graphics applications
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
On computability and some decision problems of parametric weighted finite automata
Journal of Automata, Languages and Combinatorics
Weighted finite automata: computing with different topologies
UC'11 Proceedings of the 10th international conference on Unconventional computation
Refinement of near random access video coding with weighted finite automata
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
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We continue investigations of weighted finite automata (WFA) as devices to compute real functions. Based on eigenvalues of the transition matrices of automata we provide a simple necessary condition for continuity and smoothness properties of the functions they compute. Using this condition we show that polynomials are the only smooth functions computed by WFA and that any WFA computing a polynomial of degree k must have at least k+1 states. The results answer problems left open in [7].