Simple chain grammars and languages

A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k>0, this new class of grammars is very closely related to the LL(1) and simple LL(1) grammars. In fact it can be shown that every simple chain grammar has an equivalent simple LL(1) grammar. Cover properties for simple chain grammars are investigated and a deterministic pushdown transducer which acts as a right parser for simple chain grammars is presented

Ch(k) grammars:A characterization of LL(k) languages

In this paper we introduce the class of so called Ch(k) grammars [pronounced "chain k grammars"]. This class of grammars is properly contained in the class of LR(k) grammars and it properly contains the LL(k) grammars. However, the family of Ch[k) languages coincides with the family of LL(k) languages. Nevertheless, the parsing properties of Ch(k) grammars are quite different from the parsing properties of LL(k) grammars. The class of Ch(k) grammars can be considered as a generalization of the class of simple chain grammars in the same sense as the class of LL(k) grammars is a generalization of the class of simple LL(1) grammars

Simple chain grammars

A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k, this new class of grammars is very close related to the class of LL(1) and simple LL(1) grammars. In fact it can be proved (not in this paper) that each simple chain grammar has an equivalent simple LL(1) grammar. A very simple (bottom-up) parsing method is provided. This method follows directly from the definition of a simple chain grammar and can easily be given in terms of the well-known LR(0) parsing method

On the relationship between the LL(k) and LR(k) grammars

In the literature various proofs of the inclusion of the class of LL(k) grammars into the class of LR(k) grammars can be found. Some of these proofs are not correct, others are informal, semi-formal or contain flaws. Some of them are correct but the proof is less straightforward than demonstrated here

The equivalence problem for LL- and LR-regular grammars

It will be shown that the equivalence problem for LL-regular grammars is decidable. Apart from extending the known result for LL(k) grammar equivalence to LLregular grammar equivalence, we obtain an alternative proof of the decidability of LL(k) equivalence. The equivalence prob]em for LL-regular grammars has been studied before, but not solved. Our proof that this equivalence problem is decidable is simple. However, this is mainly because we can reduce the problem to the equivalence problem for real-time strict deterministic grammlars, which is decidable

Unifying LL and LR parsing

In parsing theory, LL parsing and LR parsing are regarded to be two distinct methods. In this paper the relation between these methods is clarified.As shown in literature on parsing theory, for every context-free grammar, a so-called non-deterministic LR(0) automaton can be constructed. Here, we show, that traversing this automaton in a special way is equivalent to LL(1) parsing. This automaton can be transformed into a deterministic LR-automaton. The description of a method to traverse this automaton results into a new formulation of the LR parsing algorithm. Having obtained in this way a relationship between LL and LR parsing, the LL(1) class is characterised, using several LR-classes

Поддержка расширенных контекстно-свободных грамматик в алгоритме синтаксического анализа Generalised LL

Горохов Артем Владимирович Поддержка расширенных контекстно-свободных грамматик в алгоритме синтаксического анализа Generalised LL кандидат физико-математических наук Семен Вячеславович Григорьев Направление математика и механика, кафедра системного программирования Синтаксический анализ играет важную роль в статическом анализе программ: на этом этапе анализа создаётся структурное представление кода, над которым производится дальнейший анализ. Инструменты для генерации синтаксических анализаторов по спецификации языка автоматзируют разработку анализаторов. Обычно спецификацией служит неоднозначная грамматика в расширенной форме Бэкуса-Наура (EBNF), но большинство инструментов не могут использовать данную форму без преобразования. Автоматическое преобразование грамматик обычно приводит к снижению производительности анализа. Существуют подходы к синтаксическому анализу EBNF-грамматик, но они не допускают неоднозначностей в граматиках. С другой стороны, алгоритм Generalised LL позволяет использовать неоднозначные BNF-грамматики и показывает хорошую производительность, но не может работать с EBNF-грамматиками. В этой работе предлагается модификация алгоритма GLL, позволяющая использовать формат граматик, который тесно связан с EBNF: расширенные контекстно-свободные грамматки. Кроме того, было показано, что модификация увеличивает производительность алгоритма по сравнению с основанным на преобразовании EBNF. Использованных источников: 32 Горохов, А. В. Поддержка расширенных контекстно-свободных грамматик в алгоритме синтаксического анализа Generalised LL: выпускная квалификационная работа: защищена 09.06.2017 / Горохов Артем Владимирович. – СПб., 2017. – 37 с. – Библиография: с. 31–34.Gorokhov Artem Vladimirovich Support of extended context-free grammars in Generalised LL parsing algorithm Associate professor Semyon Grigorev. Mathematics & mechanics, software engineering department Parsing plays an important role in static program analysis: during this step a structural representation of code is created upon which further analysis is performed. Parser generator tools, being provided with syntax specification, automate parser development. Language documentation often acts as such specification. Documentation usually takes form of ambiguous grammar in Extended Backus-Naur Form which most parser generators fail to process. Automatic grammar transformation generally leads to parsing performance decrease. Some approaches support EBNF grammars natively, but they all fail to handle ambiguous grammars. On the other hand, Generalised LL parsing algorithm admits arbitrary context-free grammars and achieves good performance, but cannot handle EBNF grammars. The main contribution of this paper is a modification of GLL algorithm which can process grammars in a form which is closely related to EBNF (Extended Context-Free Grammar). We also show that the modification improves parsing performance as compared to grammar transformation-based approach. Sources cited: 32 Gorokhov, A. V. Support of extended context-free grammars in Generalised LL parsing algorithm: Graduation thesis: Defended 09.06.2017 / Gorokhov Artem Vladimirovich. – St. Petersburg., 2017. – 37 pp. – Bibliography: pp. 21-34

Structure preserving transformations on non-left-recursive grammars

We will be concerned with grammar covers, The first part of this paper presents a general framework for covers. The second part introduces a transformation from nonleft-recursive grammars to grammars in Greibach normal form. An investigation of the structure preserving properties of this transformation, which serves also as an illustration of our framework for covers, is presented