Subclasses Of Context-free Grammars Research Articles

Non-Self-Embedding Grammars and Descriptional Complexity

Non-self-embedding grammars are a subclass of context-free grammars which only generate regular languages. The size costs of the conversion of non-self-embedding grammars into equivalent finite automata are studied, by proving optimal bounds for the number of states of nondeterministic and deterministic automata equivalent to given non-self-embedding grammars. In particular, each non-self-embedding grammar of size s can be converted into an equivalent nondeterministic automaton which has an exponential size in s and into an equivalent deterministic automaton which has a double exponential size in s. These costs are shown to be optimal. Moreover, they do not change if the larger class of quasi-non-self-embedding grammars, which still generate only regular languages, is considered. In the case of letter bounded languages, the cost of the conversion of non-self-embedding grammars and quasi-non-self-embedding grammars into deterministic automata reduces to an exponential of a polynomial in s.

Язык моделирования гетерогенных динамических систем LISMA_HDS

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

Double Greibach operator grammars

Every context-free grammar can be transformed into one in double Greibach operator form, that satisfies both double Greibach form and operator form. Examination of the expressive power of various well-known subclasses of context-free grammars in double Greibach and/or operator form yields an extended hierarchy of language classes. Basic decision properties such as equivalence can be stated in stronger forms via new classes of languages in this hierarchy.