Cooperating Distributed Grammar Systems Research Articles

A novel cryptosystem based on cooperating distributed grammar systems

In language theory based cryptography, a block cipher based on Gluskov product of automata was considered and studied. On the other hand the concept of cooperating distributed grammar systems (CDGS) was introduced and studied by Csuhaj-Varju and Dassow. Motivated by this cryptosystem, we introduce a block cipher based on CDGS which has better security with regard to avalanche effect and is suitable for implementation.

A novel cryptosystem based on cooperating distributed grammar systems

In language theory based cryptography, a block cipher based on Gluškov product of automata was considered and studied. On the other hand the concept of cooperating distributed grammar systems (CDGS) was introduced and studied by Csuhaj-Varjú and Dassow. Motivated by this cryptosystem, we introduce a block cipher based on CDGS which has better security with regard to avalanche effect and is suitable for implementation.

VARIANTS OF COMPETENCE-BASED DERIVATIONS IN CD GRAMMAR SYSTEMS

In this paper we introduce and study some new cooperation protocols for cooperating distributed (CD) grammar systems. These derivation modes depend on the number of different nonterminals present in the sentential form obtained when a component finished a derivation phase. This measure describes the competence of the grammar on the string (the competence is high if the number of the different nonterminals is small). It is also a measure of the efficiency of the grammar on the given string (a component is more efficient than another one if it is able to decrease the number of nonterminals in the string to a greater extent). We prove that if the underlying derivation mode is the t-mode derivation, then some variants of these systems determine the class of random context ET0L languages. If these CD grammar systems use the k step limited derivations as underlying derivation mode, then they are able to generate any recursively enumerable language.

ON COMPETENCE IN CD GRAMMAR SYSTEMS WITH PARALLEL REWRITING

We continue our investigation of the generative power of cooperating distributed grammar systems (CDGSs), using the previously introduced ≤k-, =k-, and ≥k-competence-based cooperation strategies and context-free components that rewrite the sentential form in a parallel manner. This leads to new characterizations of the languages generated by (random context) ET0L systems and recurrent programmed grammars.

Hybrid modes in cooperating distributed grammar systems: combining the t-mode with the modes ⩽k and =k

We continue our research on hybrid derivation modes of cooperating distributed (CD) grammar systems started in (Fernau et al., Proc. 3rd Internat. Conf. Developments in Language Theory, Aristotle University of Thessaloniki, 1997, pp. 261–272; Theoret. Comput. Sci. 259 (2001) 405). Here, we focus on (hybrid) systems with context-free components working in a hybrid t- and Δk-mode, Δ∈{⩽,=}. We prove that CD grammar systems working in the mode (t∧=1), which means that each component cannot perform more than one derivation step in a row, characterize the context-free programmed languages with finite index. Moreover, we show that additional external hybridization of this mode with, e.g., the =1-mode (or =2-mode, respectively) leads to a characterization of the context-free ordered languages (or the context-free programmed languages with appearance checking, respectively). In particular, hybrid CD grammar systems with classical and internally hybrid modes have universal computational power, a result which is unknown for hybrid CD grammar systems whose components work only in classical modes, since such systems are computationally equivalent to recurrent programmed grammars with appearance checking, as shown in (Theoret. Computer. Sci. 259 (2001) 405). Furthermore, we obtain a characterization of ordered languages within the framework of CD grammar systems.

Hybrid modes in cooperating distributed grammar systems: internal versus external hybridization

We introduce several internally hybrid derivation modes of cooperating distributed (CD) grammar systems. External hybridizations were investigated by Mitrana and Păun: for example, some components of a CD grammar system, when enabled, have to work as long as possible – they work in the so-called t-mode –, and some others, when enabled, perform at least k derivation steps – this is the so-called ⩾k-mode. On the other hand, in an internally hybrid grammar system combining the t- and ⩾k-mode – we denote this combination by (t∧⩾k) – each component, when enabled, has to work as long as possible, yet performing at least k derivation steps. In this paper, among other things, we show that such externally hybrid CD grammar systems with components working in the t-mode and the ⩾k-mode, can be characterized by CD grammar systems with all components working in the (t∧⩾k)-mode, and these can be characterized by recurrent programmed grammars with appearance checking, or, as well, by ET0L systems with permitting random context.