Emergence in Context-Free Parallel Communicating Grammar Systems: What Does and Does not Make a Grammar System More Expressive Than Its Parts

2016 ◽  
pp. 171-213
Author(s):  
Stefan D. Bruda ◽  
Mary Sarah Ruth Wilkin
Keyword(s):  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Parallel Communicating Grammar Systems

ON METALINEAR PARALLEL COMMUNICATING GRAMMAR SYSTEMS

2007 ◽  
Vol 18 (06) ◽  
pp. 1313-1322
Author(s):  
ANDREAS MALCHER ◽  
BETTINA SUNCKEL
Keyword(s):  
Intermediate Model ◽  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Parallel Communicating Grammar Systems

A generalization of centralized and returning parallel communicating grammar systems with linear components (linear CPC grammar systems) is studied. It is known that linear CPC grammar systems are more powerful than regular CPC grammar systems and that CPC grammar systems with context-free components are more powerful than linear CPC grammar systems. Here, the intermediate model of metalinear CPC grammar systems is studied. This is a CPC grammar system where the master is allowed to use metalinear rules whereas the remaining components are restricted to use linear rules only. It turns out that metalinear CPC grammar systems are more powerful than linear CPC grammar systems and less powerful than CPC grammar systems with context-free components. Furthermore, it is shown that all languages generated by metalinear CPC grammar systems are semilinear.

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

2016 ◽  
Vol 26 (03) ◽  
pp. 1650012
Author(s):  
Stefan D. Bruda ◽  
Mary Sarah Ruth Wilkin
Keyword(s):  
Linear Space ◽  
Decision Problems ◽  
Analysis Tool ◽  
Context Sensitive ◽  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Parallel Communicating Grammar Systems

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.

scholarly journals Splicing Context-Free Matrix Grammars using Parallel Communicating Grammar Systems

2019 ◽  
Vol 8 (12) ◽  
pp. 1281-1283
Keyword(s):  
Dna Computing ◽  
Computational Theory ◽  
Generative Power ◽  
Grammar System ◽  
Grammar Systems ◽  
Context Free ◽  
Theoretical Results ◽  
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].

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

2016 ◽  
Vol 8 (2) ◽  
pp. 113-170
Author(s):  
Mary Sarah Ruth Wilkin ◽  
Stefan D. Bruda
Keyword(s):  
Concurrent Systems ◽  
Communication Model ◽  
Broadcast Communication ◽  
Turing Completeness ◽  
One Step ◽  
Grammar Systems ◽  
Turing Complete ◽  
Context Free ◽  
Original Construction ◽  
Parallel Communicating Grammar Systems

Abstract 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.

Pattern Languages Versus Parallel Communicating Grammar Systems

1997 ◽  
Vol 08 (01) ◽  
pp. 67-80 ◽  
Author(s):  
Sorina Dumitrescu ◽  
Gheorghe Păun ◽  
Arto Salomaa
Keyword(s):  
Pattern Languages ◽  
Grammar Systems ◽  
Context Free ◽  
Parallel Communicating Grammar Systems

We compare the power of two (fairly different) recently investigated language identifying devices: patterns and parallel communicating (PC) grammar systems. The simulation of multi-patterns by context-free PC grammar systems is rather obvious, but, unexpectedly, this can be realized also by (non-centralized) PC grammar systems with right-linear components. Moreover, infinite multi-patterns forming a regular set can also be simulated by PC grammar systems with right-linear components, whereas PC grammar systems with context-free components can simulate context-free multi-patterns with context-free domains for variables.

ON THE DESCRIPTIONAL COMPLEXITY OF METALINEAR CD GRAMMAR SYSTEMS

2005 ◽  
Vol 16 (05) ◽  
pp. 1011-1025
Author(s):  
BETTINA SUNCKEL
Keyword(s):  
Recursive Function ◽  
Trade Off ◽  
Descriptional Complexity ◽  
Grammar System ◽  
Trade Offs ◽  
Grammar Systems ◽  
Context Free ◽  
Context Free Grammars

Metalinear CD grammar systems are context-free CD grammar systems where each component consists of metalinear productions. The maximal number of nonterminals in all starting productions is referred to as the width of a CD grammar system. It is shown that between the class of CD grammar systems of width m + 1 and of width m there are savings concerning the size of the grammar system not bounded by any recursive function. This is called a non-recursive trade-off. Furthermore, it is proven that there are non-recursive trade-offs between the class of metalinear CD grammar systems of width m and the class of (2m - 1)-linear context-free grammars. In addition, some decidability results are presented.

scholarly journals Parallel Communicating String - Graph P System

2011 ◽  
Vol 10 (2) ◽  
pp. 63-74
Author(s):  
Meena Parvathy Sankar ◽  
N.G. David
Keyword(s):  
P Systems ◽  
P System ◽  
Generative Power ◽  
Grammar System ◽  
Graph Language ◽  
String Graph ◽  
Language L ◽  
Grammar Systems ◽  
Parallel Communicating Grammar Systems

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.

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