Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

An automata-theoretical characterization of the OI-hierarchy

Abstract: This paper gives an automata-theoretical characterization of the OI-hierarchy ( Damm (1982) , Engelfriet and Schmidt (1977) , Wand (1975) ). This hierarchy is generated by so-called level- n grammars which are natural generalizations from context free and macro grammars in that their nonterminals are treated as functionals of higher type, i.e., they are allowed to carry up to n levels of parameters. The automata model used for this characterization is the n -iterated pushdown automaton. Its characteristic feature is the storage structure which consists of a nesting of pushdowns up to nesting depth n . The equivalence proof is given constructively, its method is illustrated using examples. By viewing level- n grammars as modeling recursive procedures on higher types the iterated pushdown automation thus provides an operational model for the run-time behavior of procedures defined by recursion on higher types which makes the results of this paper interesting not only from a language theoretical point of view.

From English to formal specifications

Abstract: Specifications provide the foundation upon which a system can be formally developed. If a specification is wrong, then no matter what method of design is used, or what quality assurance procedures are in place, they will not result in a system that meets the requirements. The specification of a system involves people of different profiles who favour different representations. At the beginning natural language is used because the specification document acts as a contract between the user and the developers. Most of the time, the only representation that users understand and agree on is natural language. At the other end, developers find natural language specifications ambiguous and incomplete and may therefore prefer formal specifications. The transition from informal specifications to formal ones is an error prone and time consuming process. This transition must be supported to ensure that the formal specifications are consistent with the informal ones. In this research we propose an interactive approach for producing formal specifications from English specifications. The approach uses research in the area of natural language understanding to analyse English specifications in order to detect ambiguities. The method used for analysing natural language text is based on McCord’s approach. This method consists of translating natural language sentences into a logical form language representation. This helps to identify ambiguities present in natural language specifications and to identify the entities and relationships. These entities and relationships are used as a basis for producing VDM data types. We also investigate the production of data type invariants for restricted sentences and the production of some common specifications. We test our approach by implementing it in Prolog-2 and apply it to an independent case study.

A meta-language for systems architecting

Abstract: The aim of this research is to design an executable meta-language that supports system architects' modeling process by automating certain model construction, manipulation and simulation tasks. This language specifically addresses the needs in systematically communicating architects' intent with a wide range of stakeholders and to organize knowledge from various domains. Our investigation into existing architecting approaches and technologies has pointed out the need to develop a simple and intuitive, yet formal language that expresses multiple layers of abstractions, provides reflexive knowledge about the models, mechanizes data exchange and manipulation, while allow integration with legacy infrastructures. A small set of linguistic primitives, stateful objects and processes that transform them, were identified as both required and sufficient building blocks of the meta-language, specified as an Object-Process Network (OPN). To demonstrate the applicability of OPN, a software environment has been developed and applied to define meta-models of large-scale complex system architectures such as space transportation systems. OPN provides three supporting aspects of architectural modeling. As a declarative language, OPN provides a diagrammatic formal language to help architects specify the space of architectural options. As an imperative language, OPN automates the process of creating architectural option instances and computes associated performance metrics for those instances. As a simulation language, OPN uses a function-algebraic model to subsume and compose discrete, continuous, and probabilistic events within one unified execution engine. To demonstrate its practical value in large-scale engineering systems, the research applied OPN to two space exploration programs and one aircraft design problem. In our experiments, OPN was able to significantly change the modeling and architectural reasoning process by automating a number of manual model construction, manipulation, and simulation tasks. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

To CNF or not to CNF? An Efficient Yet Presentable Version of the CYK Algorithm.

Abstract: The most familiar algorithm to decide the membership problem for context-free grammars is the one by Cocke, Younger and Kasami (CYK) using grammars in Chomsky normal form (CNF). We propose to teach a simple modification of the CYK algorithm that uses grammars in a much less restrictive binary normal form (2NF) and two precomputations: the set of nullable nonterminals and the inverse of the unit relation between symbols. The modified algorithm is equally simple as the original one, but highlights that the at most binary branching rules alone are responsible for the O(n 3 ) time complexity. Moreover, the simple transformation to 2NF comes with a linear increase in grammar size, whereas some transformations to CNF found in most prominent textbooks on formal languages may lead to an exponential increase.

Evaluating formal properties of feature diagram languages

Abstract: Feature diagrams (FDs) are a family of popular modelling languages, mainly used for managing variability in software product lines. FDs were first introduced by Kang et al. as part of the feature-oriented domain analysis (FODA) method back in 1990. Since then, various extensions of FODA FDs were devised to compensate for purported ambiguity and lack of precision and expressiveness. Recently, the authors surveyed these notations and provided them with a generic formal syntax and semantics, called free feature diagrams (FFDs). The authors also started investigating the comparative semantics of FFD with respect to other recent formalisations of FD languages. Those results were targeted at improving the quality of FD languages and making the comparison between them more objective. The previous results are recalled in a self-contained, better illustrated and better motivated fashion. Most importantly, a general method is presented for comparative semantics of FDs grounded in Harel and Rumpe's guidelines for defining formal visual languages and in Krogstie et al.'s semiotic quality framework. This method being actually applicable to other visual languages, FDs are also used as a language (re)engineering exemplar throughout the paper.