Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Finite tree automata with cost functions
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Basic notions of universal algebra for language theory and graph grammars
Theoretical Computer Science
Handbook of formal languages, vol. 1
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 3
The transducers and formal tree series
Acta Cybernetica
Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Syntax-Directed Semantics: Formal Models Based on Tree Transducers
Syntax-Directed Semantics: Formal Models Based on Tree Transducers
Semirings, Automata and Languages
Semirings, Automata and Languages
Bottom-up and top-down tree series transformations
Journal of Automata, Languages and Combinatorics
Hierarchies of tree series transformations
Theoretical Computer Science
Hasse diagrams for classes of deterministic bottom-up tree-to-tree-series transformations
Theoretical Computer Science
Computational Linguistics
Tiburon: a weighted tree automata toolkit
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
Equational weighted tree transformations with discounting
Algebraic Foundations in Computer Science
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In recent investigations, tree transducers were generalized to tree series transducers [21, 8, 12] by allowing tree series as output rather than trees, where a tree series is a mapping from output trees to some semiring. The semantics of tree series transducers was defined in an algebraic framework, more precisely, as an initial algebra semantics. In this paper we suggest an alternative approach by introducing weighted tree transducers, of which the semantics is defined in an operational style. A weighted tree transducer is a tree transducer each (term rewriting) rule of which is associated with a weight taken from a semiring. Along a successful derivation the weights of the involved rules are multiplied and, for every pair of input tree and output tree, the weights of its successful derivations are summed up. We show in a constructive way that the two approaches, i.e., tree series transducers and weighted tree transducers, are semantically equivalent for both, the top-down and the bottom-up case.