Abstract
This invited talk presents the work conducted on the problems that arise when dealing with weighted automata containing \(\varepsilon \)-transitions: how to define the behaviour of such automata in which the presence of \(\varepsilon \)-circuits results in infinite summations, and second how to eliminate the \(\varepsilon \)-transitions in an automaton whose behaviour has been recognised to be well-defined. The origin of this work is the implementation, in the Awali platform [19], of an \(\varepsilon \)-transition removal algorithm for automata with weight in \(\mathbb {Q}\) or \(\mathbb {R}\), a case that had never been treated before in the rich literature on the subject of \(\varepsilon \)-transition removal algorithms (cf. [16] for a survey). The results of this work have been published in [14].
J. Sakarovitch Joint work with S. Lombardy.
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Lombardy, S., Sakarovitch, J. (2018). The Validity of Weighted Automata. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_4
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