<p> Earley's parsing algorithm is an O(n^3) algorithm for parsing according to any context-free grammar. Its theoretical importance stems from the fact that it was one of the first algorithms to achieve this time bound, but it has also seen success in compiler-compilers, theorem provers and natural language processing. It has an elegant structure, and its time complexity on restricted classes of grammars is often as good as specialized algorithms. Grammars with ϵ-productions, however, require special consideration, and have historically lead to inefficient and inelegant implementations.</p> <p> In this thesis, we develop the algorithm from specification using the B-Method. Through refinement steps, we arrive at a list-processing formulation, in which the problems with ϵ-productions emerge and can be understood. The development highlights the essential properties of the algorithm, and has also lead to the discovery of an implementation optimization. We end by giving a concept-test of the algorithm as a literate Pascal program.</p> / Thesis / Master of Computer Science (MCS)

No / The complex formation of Islamic geometric Patterns (IGP) is one of the distinctive features in Islamic art and architecture. Many have attempted to reproduce these patterns in digital form, using various pattern generation techniques. Shape grammars are an effective pattern generation method, providing good aesthetic results. In this paper we present a novel approach in generating 3D IGP using an extended shape grammar: Parametrized Shape Grammar (PSG). PSG allows a user to generate both original and novel forms of Islamic geometric motifs (a repeated unit of a pattern). PSG is generalized to generate n-fold Islamic geometric motifs in a 3D environment, practically implemented as a 3D modeling tool within Autodesk Maya. The parametrization within each grammar rule is the key to generating numerous original and novel Islamic geometric motifs.

The library was one of the most important institutions in the Hellenistic and Roman city, as evidenced in the writings of ancient authors, and the building remains of libraries found throughout the Greco-Roman world, from Asia Minor to France and from Africa to Northern Greece. Yet, the library remains one of the least easily identifiable building forms and one of the most difficult to reconstruct, because unlike architectural types such as the temple, stoa, or theater, the library exhibits significant variety in design, scale and monumentality and the use of different component elements. In reconstructing libraries, scholars often rely on a prescribed set of assumptions about components and their arrangement that limit our ability to identify libraries and understand their diversity of arrangement. This dissertation proposes shape grammars as an effective computational methodology to identify, understand, and reconstruct ancient libraries of diverse and variant scale, design and monumentality. The work presents a comprehensive documentation of known and identified libraries, reviews the design principles of the architectural form of ancient libraries, and on the basis of this historical analysis proposes a shape grammar for the formal specification of ancient Greek and Roman libraries. The library grammar encodes the design principles of ancient libraries in ninety-one rules that are grouped in two major parts: the first generates the main hall of the library and its interior design, and the second generates the complete layout of the library including additional porticoes, peristyles, exedras, gardens and propylon. The application of the rules generates libraries of diverse scales and monumentality: libraries known in the corpus and as well as hypothetical libraries. The dissertation presents grammatical derivations for the seventeen known and identified libraries. These derivations, depending on the degree of preservation of the building remains of libraries, function as an evaluative tool for the validity of the grammar or for the reconstructions proposed by traditional research. In many cases, they point to different possibilities in the identification of the building remains related to libraries among remains of different phases or remains belonging to neighboring buildings, and suggest variant scenarios of reconstruction that might not stand out using traditional techniques of reconstruction. The metadata of the rules in the grammar and the derivations are used in a frequency analysis that provides a probabilistic model as an effective and systematic guide in identifying, evaluating and predicting the architectural form of libraries: the main hall and the threshold are identified as mandatory architectural components, the niches and focal point as most likely, and the podium with a colonnade as less likely to occur in a library. Less frequently, the library is a whole complex with exedras, a monumental entry and additional rooms that function as auditoria, banquet halls or offices. Moreover, the work presents the derivations of possible libraries and evaluates the rules applied to generate them based on the frequency analysis. In the end, the work concludes whether these buildings are libraries, non-libraries or exceptional libraries. Lastly, this dissertation assesses the opportunities and challenges that emerge in using shape grammars to identify and reconstruct libraries and also the value and impact of using formal computational methods in the systematic exploration of variations in reconstruction of the archaeological record.

The purpose of this dissertation is to develop a new generative grammar, based on the principles of intensional logic. More specifically, the goal is to create a psychologically real grammar model for use in natural language processing. The new grammar consists of a set of context-free rewrite rules tagged with intensional versions. Most generative grammars, such as transformational grammar, lexical functional-grammar and head-driven phrase structure grammar, extend traditional context-free grammars with a mechanism for dealing with contextual information, such as subcategorization of words and agreement between different phrasal elements. In these grammars there is not enough separation between the utterances of a language and the context in which they are uttered. Their models of language seem to assume that context is in some way encapsulated in the words of the language instead of the other way around. In intensional logic, the truth of a statement is considered in the context in which it is uttered, unlike traditional predicate logic in which truth is assigned in a vacuum, regardless of when or where it may have been stated. To date, the application of the principles of intensionality to natural languages has been confined to semantic theory. We remedy this by applying the ideas of intensional logic to syntactic context, resulting in intensional context-free grammar. Our grammar takes full advantage of the simplicity and elegance of context-free grammars while accounting for information that is beyond the sentence itself, in a realistic way. Sentence derivation is entirely encapsulated in the context of its utterance. In fact, for any particular context, the entire language of the grammar is encapsulated in that context. This is evidenced by our proof that the language of an intensional grammar is a set of context-free languages, indexed by context. To further support our claims we design and implement a small fragment of English using the grammar. The English grammar is capable of generating both passive and active sentences that include a subject, verb and up to two optional objects. Furthermore, we have implemented a partial French to English translation system that uses a single language dimension to initiate a translation. This allows us to include multiple languages in one grammar, unlike other systems which must separate the grammars of each language. This result has led this author to believe that we have created a grammar that is a viable candidate for a true Universal Grammar, far exceeding our initial goals. / Graduate / 0984 / 0800 / 0290 / rlittle@uvic.ca

This thesis presents work done on compressed graph representations via hyperedge replacement grammars. It comprises two main parts. Firstly the RePair compression scheme, known for strings and trees, is generalized to graphs using graph grammars. Given an object, the scheme produces a small context-free grammar generating the object (called a “straight-line grammar”). The theoretical foundations of this generalization are presented, followed by a description of a prototype implementation. This implementation is then evaluated on real-world and synthetic graphs. The experiments show that several graphs can be compressed stronger by the new method, than by current state-of-the-art approaches. The second part considers algorithmic questions of straight-line graph grammars. Two algorithms are presented to traverse the graph represented by such a grammar. Both algorithms have advantages and disadvantages: the first one works with any grammar but its runtime per traversal step is dependent on the input grammar. The second algorithm only needs constant time per traversal step, but works for a restricted class of grammars and requires quadratic preprocessing time and space. Finally speed-up algorithms are considered. These are algorithms that can decide specific problems in time depending only on the size of the compressed representation, and might thus be faster than a traditional algorithm would on the decompressed structure. The idea of such algorithms is to reuse computation already done for the rules of the grammar. The possible speed-ups achieved this way is proportional to the compression ratio of the grammar. The main results here are a method to answer “regular path queries”, and to decide whether two grammars generate isomorphic 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.

Tato disertační práce zavádí jednostranné gramatiky s nahodilým kontextem jako řízené gramatiky založené na bezkontextových gramatikách. V těchto gramatikách je ke každému pravidlu přiřazena množina povolujících symbolů a množina zakazujících symbolů a množina pravidel je rozdělena na množinu levých pravidel s nahodilým kontextem a množinu pravých pravidel s nahodilým kontextem . Levým pravidlem s nahodilým kontextem lze přepsat neterminál pokud se všechny povolující symboly vyskytují vlevo od přepisovaného neterminálu a žádný zakazující symbol tam přítomen není. Pravé pravidlo s nahodilým kontextem lze aplikovat analogicky, ale ona kontrola na přítomnost a nepřítomnost symbolů je provedena doprava od přepisovaného neterminálu. Práce je rozdělena na tři části. První část uvádí motivaci za zavedením jednostranných gramatik s nahodilým kontextem a umisťuje materiál pokrytý v této práci do vědeckého kontextu. Poté dává přehled základů teorie formálních jazyků a některých méně známých oblastí, jejichž znalost je nutná pro pochopení studovaného tématu. Druhá část tvoří jádro práce. Formálně definuje jednostranné gramatiky s nahodilým kontextem a studuje je z mnoha pohledů. Mezi studovaná témata patří generativní síla, vztah k jiným typům gramatik, redukce, normální formy, nejlevější derivace, zobecněné a LL verze těchto gramatiky. Třetí část této práce zakončuje diskusi několika poznámkami. Mezi ně patří poznámky týkající se aplikovatelnosti zavedených gramatik v praxi, bibliografie a otevřených problémů.

Este trabalho descreve o formalismo das gramáticas livres de contexto adaptativas com verificação de aparência. Esses dispositivos gramaticais possuem como núcleo uma gramática livre de contexto subjacente e, como mecanismo de auto-modificação, uma ou várias funções adaptativas que determinam quais produções são aplicáveis em cada passo de uma derivação. A verificação de aparência se refere a uma forma especial de aplicar algumas produções, escolhidas pelo projetista da gramática, sem alterar a forma sentencial nessa aplicação. É provado que esse formalismo tem poder de máquina de Turing demonstrando, em forma construtiva, sua equivalência com quatro formalismos gramaticais baseados em gramáticas livres de contexto com mecanismos de controle, que tem esse poder. São desenvolvidos dois analisadorers para linguagens dependentes de contexto a partir de um desses outros quatro formalismos. Um deles, que é baseado em autômatos-pilha, opera em forma ascendente; o outro, baseado em autômatos finitos adaptativos, opera em forma descendente. / This work introduces and describes the formalism of the context-free adaptive grammar with appearance checking. Such gramatical devices have as its kernel a subjacent context-free grammar and, as mechanism of self-modification, one or several adaptive functions which determines the productions able to be applied at each step of a derivation. The appearance checking refers to a special way to apply some productions, choosen by the designer of the grammar, without changing the sentential form in this application. It is proved that this formalism has Turing Machine power, proving, by construction, its equivalence with four grammatical formalisms based on context-free grammars and with control mechanisms, with such power. Two parsers have been developed for context-dependent languages from one of these four formalisms. One of them is based on stack-automata, and operates in a bottom-up fashion.

Este trabalho descreve o formalismo das gramáticas livres de contexto adaptativas com verificação de aparência. Esses dispositivos gramaticais possuem como núcleo uma gramática livre de contexto subjacente e, como mecanismo de auto-modificação, uma ou várias funções adaptativas que determinam quais produções são aplicáveis em cada passo de uma derivação. A verificação de aparência se refere a uma forma especial de aplicar algumas produções, escolhidas pelo projetista da gramática, sem alterar a forma sentencial nessa aplicação. É provado que esse formalismo tem poder de máquina de Turing demonstrando, em forma construtiva, sua equivalência com quatro formalismos gramaticais baseados em gramáticas livres de contexto com mecanismos de controle, que tem esse poder. São desenvolvidos dois analisadorers para linguagens dependentes de contexto a partir de um desses outros quatro formalismos. Um deles, que é baseado em autômatos-pilha, opera em forma ascendente; o outro, baseado em autômatos finitos adaptativos, opera em forma descendente. / This work introduces and describes the formalism of the context-free adaptive grammar with appearance checking. Such gramatical devices have as its kernel a subjacent context-free grammar and, as mechanism of self-modification, one or several adaptive functions which determines the productions able to be applied at each step of a derivation. The appearance checking refers to a special way to apply some productions, choosen by the designer of the grammar, without changing the sentential form in this application. It is proved that this formalism has Turing Machine power, proving, by construction, its equivalence with four grammatical formalisms based on context-free grammars and with control mechanisms, with such power. Two parsers have been developed for context-dependent languages from one of these four formalisms. One of them is based on stack-automata, and operates in a bottom-up fashion.

This work presents a new test case generation methodology, which has a high degree of automation (cost reduction); while providing increased power in terms of defect detection (benefits increase). Our solution is a variation of model-based testing, which takes advantage of symbolic grammars (a context-free grammar where terminals are replaced by regular expressions that represent their solution space) and quasi-random sequences to generate test cases. Previous test case generation techniques are enhanced with adaptive random testing to maximize input space coverage; and selective and directed sentence generation techniques to optimize sentence generation. Our solution was tested by generating 200 firewall policies containing up to 20 000 rules from a generic firewall grammar. Our results show how our system generates test cases with superior coverage of the input space, increasing the probability of defect detection while reducing considerably the needed number the test cases compared with other previously used approaches. / Software Engineering and Intelligent Systems