Two iteration theorems for the LL(k) languages

AbstractThe structure of derivation trees over an LL(k) grammar is explored and a property of these trees obtained which is shown to characterize the LL(k) grammars. This characterization, called the LL(k) Left Part Theorem, makes it possible to establish a pair of iteration theorems for the LL(k) languages. These theorems provide a general and powerful method of showing that a language is not LL(k) when that is the case. They thus provide for the first time a flexible tool with which to explore the structure of the LL(k) languages and with which to discriminate between the LL(k) and LR(k) language classes.Examples are given of LR(k) languages which, for various reasons, fail to be LL(k). Easy and rigorous proofs to this effect are given using our LL(k) iteration theorems. In particular, it is proven that the dangling-ELSE construct allowed in PL/I and Pascal cannot be generated by any LL(k) grammar. We also give a new and straightforward proof based on the LL(k) Left Part Theorem that every LL(k) grammar is LR(k)

Iterációs Lemmák a Formális Nyelvek Elméletében

A dolgozat témája reguláris és környezetfüggetlen nyelvekre vonatkozó iterációs lemmák ismertetése, összehasonlítása.B

Intercalation properties of context-free languages

Context-freedom of a language implies certain intercalation properties known as pumping or iteration lemmas. Although the question of a converse result for some of the properties has been studied, it is still not entirely clear how these properties are related, which are the stronger ones and which are weaker;Among the intercalation properties for context-free languages the better known are the general pumping conditions (generalized Ogden\u27s, Ogden\u27s and classic pumping conditions), Sokolowski-type conditions (Sokolowski\u27s and Extended Sokolowski\u27s conditions) and the Interchange condition. We present a rather systematic investigation of the relationships among these properties; it turns out that the three types of properties, namely pumping, Sokolowski-type and interchange, above are independent. However, the interchange condition is strictly stronger than the Sokolowski\u27s condition;Intercalation properties of some subclasses of context-free languages are also studied. We prove a pumping lemma and an Ogden\u27s lemma for nonterminal bounded languages and show that none of these two conditions is sufficient. We also investigate three of Igarashi\u27s pumping conditions for real-time deterministic context-free languages and show that these conditions are not sufficient either. Furthermore, we formulate linear analogues of the general pumping and interchange conditions and then compare them to the general context-free case. The results show that these conditions are also independent

Grammars with Restricted Derivation Trees

V této disertační práci jsou studovány teoretické vlastnosti gramatik s omezenými derivačními stromy. Po uvedení současného stavu poznání v této oblasti je výzkum zaměřen na tři základní typy omezení derivačních stromů. Nejprve je představeno zcela nové téma, které je založeno na omezení řezů a je zkoumána vyjadřovací síla takto omezené gramatiky. Poté je zkoumáno několik nových vlastností omezení kladeného na cestu derivačních stromů. Zejména je studován vliv vymazávacích pravidel na vyjadřovací sílu gramatik s omezenou cestou a pro tyto gramatiky jsou zavedeny dvě normální formy. Následně je popsána nová souvislost mezi gramatikami s omezenou cestou a některými pseudouzly. Dále je prezentován protiargument k vyjadřovací síle tohoto modelu, která byla dosud považována za dobře známou vlastnost. Nakonec je zavedeno zobecnění modelu s omezenou cestou na ne jednu, ale několik cest. Tento model je následně studován zejména z hlediska vlastností vkládání, uzávěrových vlastností a vlastností syntaktické analýzy.This doctoral thesis studies theoretical properties of grammars with restricted derivation trees. After presenting the state of the art concerning this investigation area, the research is focused on the three main kinds of the restrictions placed upon the derivation trees. First, it introduces completely new investigation area represented by cut-based restriction and examines the generative power of the grammars restricted in this way. Second, it investigates several new properties of path-based restriction placed upon the derivation trees. Specifically, it studies the impact of erasing productions on the generative power of grammars with restricted path and introduces two corresponding normal forms. Then, it describes a new relation between grammars with restricted path and some pseudoknots. Next, it presents a counterargument to the generative power of grammars with controlled path that has been considered as well-known so far. Finally, it introduces a generalization of path-based restriction to not just one but several paths. The model generalized in this way is studied, namely its pumping, closure, and parsing properties.