Splicing Context-Free Matrix Grammars using Parallel Communicating Grammar Systems

Extensive research on splicing of strings in DNA computing has established important theoretical results in computational theory. Further, splicing on strings has been extended to arrays in[2]. In this context, we propose, a grammar system, using queries to splice context-free matrix grammars and show that the language generated by this grammar system is incomparable to the language given in [3] and has more generative power than in [2].

Parallel communicating grammar systems with context-free components are Turing complete for any communication model

Parallel Communicating Grammar Systems (PCGS) were introduced as a language-theoretic treatment of concurrent systems. A PCGS extends the concept of a grammar to a structure that consists of several grammars working in parallel, communicating with each other, and so contributing to the generation of strings. PCGS are usually more powerful than a single grammar of the same type; PCGS with context-free components (CF-PCGS) in particular were shown to be Turing complete. However, this result only holds when a specific type of communication (which we call broadcast communication, as opposed to one-step communication) is used. We expand the original construction that showed Turing completeness so that broadcast communication is eliminated at the expense of introducing a significant number of additional, helper component grammars. We thus show that CF-PCGS with one-step communication are also Turing complete. We introduce in the process several techniques that may be usable in other constructions and may be capable of removing broadcast communication in general.

Limitations of Coverability Trees for Context-Free Parallel Communicating Grammar Systems and Why these Grammar Systems are not Linear Space

Coverability trees offer a finite characterization of all the derivations of a context-free parallel grammar system (CF-PCGS). Their finite nature implies that they necessarily omit some information about these derivations. We demonstrate that the omitted information is most if not all of the time too much, and so coverability trees are not useful as an analysis tool except for their limited use already considered in the paper that introduces them (namely, determining the decidability of certain decision problems over PCGS). We establish this result by invalidating an existing proof that synchronized CF-PCGS are less expressive than context-sensitive grammars. Indeed, we discover that this proof relies on coverability trees for CF-PCGS, but that such coverability trees do not in fact contain enough information to support the proof.

ON CENTRALIZED PARALLEL COMMUNICATING GRAMMAR SYSTEMS WITH CONTEXT-SENSITIVE COMPONENTS

Centralized parallel communicating grammar systems with context-sensitive components that work in returning mode can only generate context-sensitive languages. Here we show that, when working in nonreturning mode, these grammar systems generate all languages from the nondeterministic time complexity class NEXT = ∪c ≥ 1 NTIME (2c·n).

Parallel Communicating String - Graph P System

The concept of parallel communicating grammar systems generating string languages is extended to string-graph P systems and their generative power is studied. It is also established that for every language L generated by a parallel communicating grammar system there exists an equivalent parallel communicating string-graph P system generating the string-graph language corresponding to L.