A survey of normal form covers for context-free grammars

An overview is given of cover results for normal forms of context-free grammars. The emphasis in this paper is on the possibility of constructing ɛ-free grammars, non-left-recursive grammars and grammars in Greibach normal form. Among others it is proved that any ɛ-free context-free grammar can be right covered with a context-free grammar in Greibach normal form. All the cover results concerning the ɛ-free grammars, the non-left-recursive grammars and the grammars in Greibach normal form are listed, with respect to several types of covers, in a cover-table

Symbolic Priors for RNN-based Semantic Parsing

International audienceSeq2seq models based on Recurrent Neural Networks (RNNs) have recently received a lot of attention in the domain of Semantic Parsing. While in principle they can be trained directly on pairs (natural language utterances, logical forms), their performance is limited by the amount of available data. To alleviate this problem, we propose to exploit various sources of prior knowledge: the well-formedness of the logical forms is modeled by a weighted context-free grammar; the likelihood that certain entities present in the input utterance are also present in the logical form is modeled by weighted finite-state automata. The grammar and automata are combined together through an efficient intersection algorithm to form a soft guide (" background ") to the RNN. We test our method on an extension of the Overnight dataset and show that it not only strongly improves over an RNN base-line, but also outperforms non-RNN models based on rich sets of hand-crafted features

Graph grammars with string-regulated rewriting

Multicellular organisms undergo a complex developmental process, orchestrated by the genetic information in their cells, in order to form a newborn individual from a fertilized egg. This complex process, not completely understood yet, is believed to have a key role in generating the impressive biotic diversity of organisms found on earth. Inspired by mechanisms of Eukaryotic genetic expression, we propose and analyse graph grammars with string-regulated rewriting. In these grammatical systems a genome sequence is represented by a regulatory string, a graph corresponds to an organism, and a set of graph grammar rules represents different forms of implementing cell division. Accordingly, a graph derivation by the graph grammar resembles the developmental process of an organism. We give examples of the concept and compare its generative power to the power of the traditional context-free graph grammars. We demonstrate that the power of expression increases when genetic regulation is included in the model, as compared to non-regulated grammars. Additionally, we propose a hierarchy of string-regulated graph grammars, arranged by expressive power. These results highlight the key role that the transmission of regulatory information during development has in the emergence of biological diversity.D.L. was supported in part by a research stay fellowship at Otto-von-Guericke-Universität Magdeburg from the Spanish Ministerio de Educación

A Lightweight Framework for Universal Fragment Composition

Domain-specific languages (DSLs) are useful tools for coping with complexity in software development. DSLs provide developers with appropriate constructs for specifying and solving the problems they are faced with. While the exact definition of DSLs can vary, they can roughly be divided into two categories: embedded and non-embedded. Embedded DSLs (E-DSLs) are integrated into general-purpose host languages (e.g. Java), while non-embedded DSLs (NE-DSLs) are standalone languages with their own tooling (e.g. compilers or interpreters). NE-DSLs can for example be found on the Semantic Web where they are used for querying or describing shared domain models (ontologies). A common theme with DSLs is naturally their support of focused expressive power. However, in many cases they do not support non–domain-specific component-oriented constructs that can be useful for developers. Such constructs are standard in general-purpose languages (procedures, methods, packages, libraries etc.). While E-DSLs have access to such constructs via their host languages, NE-DSLs do not have this opportunity. Instead, to support such notions, each of these languages have to be extended and their tooling updated accordingly. Such modifications can be costly and must be done individually for each language. A solution method for one language cannot easily be reused for another. There currently exist no appropriate technology for tackling this problem in a general manner. Apart from identifying the need for a general approach to address this issue, we extend existing composition technology to provide a language-inclusive solution. We build upon fragment-based composition techniques and make them applicable to arbitrary (context-free) languages. We call this process for the composition techniques’ universalization. The techniques are called fragment-based since their view of components— reusable software units with interfaces—are pieces of source code that conform to an underlying (context-free) language grammar. The universalization process is grammar-driven: given a base language grammar and a description of the compositional needs wrt. the composition techniques, an adapted grammar is created that corresponds to the specified needs. The result is thus an adapted grammar that forms the foundation for allowing to define and compose the desired fragments. We further build upon this grammar-driven universalization approach to allow developers to define the non–domain-specific component-oriented constructs that are needed for NE-DSLs. Developers are able to define both what those constructs should be, and how they are to be interpreted (via composition). Thus, developers can effectively define language extensions and their semantics. This solution is presented in a framework that can be reused for different languages, even if their notion of ‘components’ differ. To demonstrate the approach and show its applicability, we apply it to two Semantic Web related NE-DSLs that are in need of component-oriented constructs. We introduce modules to the rule-based Web query language Xcerpt and role models to the Web Ontology Language OWL

Nonterminal Separating Macro Grammars

We extend the concept of nonterminal separating (or NTS) context-free grammar to nonterminal separating $m$-macro grammar where the mode of derivation $m$ is equal to "unrestricted". "outside-in' or "inside-out". Then we show some (partial) characterization results for these NTS $m$-macro grammars

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Recently, it has been shown that every recursively enumerable language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maximal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors

An approach to computing downward closures

The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property. This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom