Numbers and Languages

The thesis presents results obtained during the authors PhD-studies. First systems of language equations of a simple form consisting of just two equations are proved to be computationally universal. These are systems over unary alphabet, that are seen as systems of equations over natural numbers. The systems contain only an equation X+A=B and an equation X+X+C=X+X+D, where A, B, C and D are eventually periodic constants. It is proved that for every recursive set S there exists natural numbers p and d, and eventually periodic sets A, B, C and D such that a number n is in S if and only if np+d is in the unique solution of the abovementioned system of two equations, so all recursive sets can be represented in an encoded form. It is also proved that all recursive sets cannot be represented as they are, so the encoding is really needed. Furthermore, it is proved that the family of languages generated by Boolean grammars is closed under injective gsm-mappings and inverse gsm-mappings. The arguments apply also for the families of unambiguous Boolean languages, conjunctive languages and unambiguous languages. Finally, characterizations for morphisims preserving subfamilies of context-free languages are presented. It is shown that the families of deterministic and LL context-free languages are closed under codes if and only if they are of bounded deciphering delay. These families are also closed under non-codes, if they map every letter into a submonoid generated by a single word. The family of unambiguous context-free languages is closed under all codes and under the same non-codes as the families of deterministic and LL context-free languages.Siirretty Doriast

A language-theoretic view on network protocols

Input validation is the first line of defense against malformed or malicious inputs. It is therefore critical that the validator (which is often part of the parser) is free of bugs. To build dependable input validators, we propose using parser generators for context-free languages. In the context of network protocols, various works have pointed at context-free languages as falling short to specify precisely or concisely common idioms found in protocols. We review those assessments and perform a rigorous, language-theoretic analysis of several common protocol idioms. We then demonstrate the practical value of our findings by developing a modular, robust, and efficient input validator for HTTP relying on context-free grammars and regular expressions

A Model Driven Approach to Model Transformations

The OMG's Model Driven Architecture (MDA) initiative has been the focus of much attention in both academia and industry, due to its promise of more rapid and consistent software development through the increased use of models. In order for MDA to reach its full potential, the ability to manipulate and transform models { most obviously from the Platform Independent Model (PIM) to the Platform Specific Models (PSM) { is vital. Recognizing this need, the OMG issued a Request For Proposals (RFP) largely concerned with finding a suitable mechanism for trans- forming models. This paper outlines the relevant background material, summarizes the approach taken by the QVT-Partners (to whom the authors belong), presents a non-trivial example using the QVT-Partners approach, and finally sketches out what the future holds for model transformations

生化学反応による計算能力の研究

早大学位記番号:新6514早稲田大

On state-alternating context-free grammars

AbstractState-alternating context-free grammars are introduced, and the language classes obtained from them are compared to the classes of the Chomsky hierarchy as well as to some well-known complexity classes. In particular, state-alternating context-free grammars are compared to alternating context-free grammars (Theoret. Comput. Sci. 67 (1989) 75–85) and to alternating pushdown automata. Further, various derivation strategies are considered, and their influence on the expressive power of (state-) alternating context-free grammars is investigated