Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results

Learnability and Overgeneration in Computational Syntax

This paper addresses the hypothesis that unnatural patterns generated by grammar formalisms can be eliminated on the grounds that they are unlearnable. I consider three examples of formal languages thought to represent dependencies unattested in natural language syntax, and show that all three can be learned by grammar induction algorithms following the Distributional Learning paradigm of Clark and Eyraud (2007). While learnable language classes are restrictive by necessity (Gold, 1967), these facts suggest that learnability alone may be insufficient for addressing concerns of overgeneration in syntax

Iterating iterated substitution

By iterating iterated substitution not all regular languages can be copied. Hence the smallest full hyper (1)-AFL is properly contained in ETOL, the smallest full hyper-AFL. The number of iterations of iterated substitution gives rise to a proper hierarchy. Consequently the smallest full hyper (1)-AFL is not a full principal AFL

An automata characterisation for multiple context-free languages

We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted at the 20th International Conference on Developments in Language Theory (DLT 2016

Generalising tree traversals and tree transformations to DAGs:Exploiting sharing without the pain

We present a recursion scheme based on attribute grammars that can be transparently applied to trees and acyclic graphs. Our recursion scheme allows the programmer to implement a tree traversal or a tree transformation and then apply it to compact graph representations of trees instead. The resulting graph traversal or graph transformation avoids recomputation of intermediate results for shared nodes – even if intermediate results are used in different contexts. Consequently, this approach leads to asymptotic speedup proportional to the compression provided by the graph representation. In general, however, this sharing of intermediate results is not sound. Therefore, we complement our implementation of the recursion scheme with a number of correspondence theorems that ensure soundness for various classes of traversals. We illustrate the practical applicability of the implementation as well as the complementing theory with a number of examples

Learning Repetition, but not Syllable Reversal

Reduplication is common, but analogous reversal processes are rare, even though reversal, which involves nested rather than crossed dependencies, is less complex on the Chomsky hierarchy. We hypothesize that the explanation is that repetitions can be recognized when they match and reactivate a stored trace in short-term memory, but recognizing a reversal requires rearranging the input in working memory before attempting to match it to the stored trace. Repetitions can thus be recognized, and repetition patterns learned, implicitly, whereas reversals require explicit, conscious awareness. To test these hypotheses, participants were trained to recognize either a reduplication or a syllable-reversal pattern, and then asked to state the rule. In two experiments, above-chance classification performance on the Reversal pattern was confined to Correct Staters, whereas above-chance performance on the Reduplication pattern was found with or without correct rule-stating. Final proportion correct was positively correlated with final response time for the Reversal Correct Staters but no other group. These results support the hypothesis that reversal, unlike reduplication, requires conscious, time-consuming computation

TDL--- A Type Description Language for Constraint-Based Grammars

This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning over types and allows for partitions and incompatible types. Working with partially as well as with fully expanded types is possible. Efficient reasoning in \tdl\ is accomplished through specialized modules.Comment: Will Appear in Proc. COLING-9