Handbook of theoretical computer science (vol. B)
Handbook of formal languages, vol. 3
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
Descriptive Approach to Language - Theoretic Complexity
Descriptive Approach to Language - Theoretic Complexity
Some Notes on the Formal Properties of Bidirectional Optimality Theory
Journal of Logic, Language and Information
An operational and denotational approach to non-context-freeness
Theoretical Computer Science - Algebraic methods in language processing
Tree-oriented proofs of some theorems on context-free and indexed languages
STOC '70 Proceedings of the second annual ACM symposium on Theory of computing
Optimality theory and the generative complexity of constraint violability
Computational Linguistics
Recursion by optimization: on the complexity of bidirectional optimality theory
Natural Language Engineering
Representing constraints with automata
ACL '98 Proceedings of the 35th Annual Meeting of the Association for Computational Linguistics and Eighth Conference of the European Chapter of the Association for Computational Linguistics
The proper treatment of optimality in computational phonology: plenary talk
FSMNLP '09 Proceedings of the International Workshop on Finite State Methods in Natural Language Processing
On the Generative Power of Multiple Context-Free Grammars and Macro Grammars
IEICE - Transactions on Information and Systems
IWPT '09 Proceedings of the 11th International Conference on Parsing Technologies
Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars
Journal of Logic, Language and Information
Restarting tree automata and linear context-free tree languages
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Some interdefinability results for syntactic constraint classes
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
The Equivalence of Tree Adjoining Grammars and Monadic Linear Context-free Tree Grammars
Journal of Logic, Language and Information
Reference-Set constraints as linear tree transductions via controlled optimality systems
FG'10/FG'11 Proceedings of the 15th and 16th international conference on Formal Grammar
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Context-free tree grammars, originally introduced by Rounds [Math. Systems Theory 4(3) (1970) 257-287], are powerful grammar devices for the definition of tree languages. The properties of the class of context-free tree languages have been studied for more than three decades now. Particularly important here is the work by Engelfriet and Schmidt [J. Comput. System Sci. 15(3) (1977) 328-353, 16(1) (1978) 67-99]. In the present paper, we consider a subclass of the class of context-free tree languages, namely the class of linear context-free tree languages. A context-free tree grammar is linear, if no rule permits the copying of subtrees. For this class of linear context-free tree languages we show that the grammar derivation mode, which is very important for the general class of context-free tree languages, is immaterial. The main result we present is the closure of the class of linear context-free tree languages under linear frontier-to-root tree transduction mappings. Two further results are the closure of this class under linear root-to-frontier tree transduction mappings and under intersection with regular tree languages.The results of the first part of the paper are applied to the formalisation of optimality theory. Optimality theory (OT), introduced by Prince and Smolensky [Tech. Report 1993], is a linguistic framework in which the mapping of one level of linguistic representation to another is based on rules and filters. The rules generate candidate expressions in the target representation, which are subsequently checked against the filters, so that only those candidates remain that survive this filtering process. A proposal to formalise the description of OT using formal language theory and in particular automata theory was presented by Karttunen [Proceedings of International Workshop on Finite-State Methods in Natural Language Processing, 1998, pp. 1-12] and Frank and Satta [Comput. Linguistics 24 (1998) 307-315]. The main result of these papers is that if the generator is defined as a finite-state string transducer and the filters are defined by finite-state string automata, then the whole OT-system can be defined by means of a finite-state string transducer. Considering the fact that most parts of linguistics have trees as their underlying data structures instead of strings, we show here that generators can be extended to linear frontier-to-root tree transducers on linear context-free tree languages--with constraints being regular tree languages--while the computation of optimal candidates can still be performed using finite-state techniques (over trees).