Semirings, automata, languages
Semirings, automata, languages
The transducers and formal tree series
Acta Cybernetica
Information and Computation
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Bottom-up and top-down tree series transformations
Journal of Automata, Languages and Combinatorics
Full Abstract Families of Tree Series I
Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa
Determinization of finite state weighted tree automata
Journal of Automata, Languages and Combinatorics
Generalized2 sequential machine maps
Journal of Computer and System Sciences
Tiburon: a weighted tree automata toolkit
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
The power of tree series transducers of type i and II
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Hierarchies of tree series transformations revisited
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
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We investigate the tree-series-to-tree-series (ts-ts) transformation computed by tree series transducers. Unless the used semiring is complete, this transformation is, in general, not well-defined. In practice, many used semirings are not complete (like the probability semiring). We establish a syntactical condition that guarantees well-definedness of the ts-ts transformation in arbitrary commutative semirings. For positive (ie, zero-sum and zero-divisor free) semirings the condition actually characterizes the well-definedness, so that well-definedness is decidable in this scenario.