CD GRAMMAR SYSTEMS WITH REGULAR START CONDITIONS

2008 ◽  
Vol 19 (04) ◽  
pp. 767-779
Author(s):  
RUDOLF FREUND ◽  
MARION OSWALD
Keyword(s):  
Finite Index ◽  
Hybrid Mode ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
The Family ◽  
Grammar Systems ◽  
Regular Sets ◽  
Classical Derivation ◽  
Recursively Enumerable Languages

We consider cooperating distributed grammar systems with the components working in different derivation modes as well as with regular sets as additional start conditions for the components. With the classical derivation modes ≤ k and = k as well as with the internally hybrid mode (≥ ℓ∧ ≤ k) we obtain a characterization of the family of recursively enumerable languages even with only one component, with the derivation modes *, t, and ≥ k as well as with the internally hybrid mode (t∧ ≥ k) two components working in the same mode and only one common regular set for both components yield computational completeness. For the internally hybrid modes (t∧ ≤ k) and (t∧ = k) we only obtain languages of finite index, but combining one component working in one of these modes (t∧ ≤ k) and (t∧ = k) with a component working in one of the modes * and ≥ k we again obtain a characterization of the family of recursively enumerable languages.

scholarly journals Adding Matrix Control: Insertion-Deletion Systems with Substitutions III

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 131
Author(s):  
Martin Vu ◽  
Henning Fernau
Keyword(s):  
Turing Machines ◽  
Biological Mechanisms ◽  
Computational Completeness ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Short Program ◽  
Matrix Control ◽  
Recursively Enumerable Languages

Insertion-deletion systems have been introduced as a formalism to model operations that find their counterparts in ideas of bio-computing, more specifically, when using DNA or RNA strings and biological mechanisms that work on these strings. So-called matrix control has been introduced to insertion-deletion systems in order to enable writing short program fragments. We discuss substitutions as a further type of operation, added to matrix insertion-deletion systems. For such systems, we additionally discuss the effect of appearance checking. This way, we obtain new characterizations of the family of context-sensitive and the family of recursively enumerable languages. Not much context is needed for systems with appearance checking to reach computational completeness. This also suggests that bio-computers may run rather traditionally written programs, as our simulations also show how Turing machines, like any other computational device, can be simulated by certain matrix insertion-deletion-substitution systems.

Jumping Grammars

2015 ◽  
Vol 26 (06) ◽  
pp. 709-731 ◽  
Author(s):  
Zbyněk Křivka ◽  
Alexander Meduna
Keyword(s):  
Finite Index ◽  
Open Problems ◽  
Generative Power ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

This paper introduces and studies jumping grammars, which represent a grammatical counterpart to the recently introduced jumping automata. These grammars are conceptualized just like classical grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. More precisely, a jumping grammar rewrites a string z according to a rule x → y in such a way that it selects an occurrence of x in z, erases it, and inserts y anywhere in the rewritten string, so this insertion may occur at a different position than the erasure of x. The paper concentrates its attention on investigating the generative power of jumping grammars. More specifically, it compares this power with that of jumping automata and that of classical grammars. A special attention is paid to various context-free versions of jumping grammars, such as regular, right-linear, linear, and context-free grammars of finite index. In addition, we study the semilinearity of context-free, context-sensitive, and monotonous jumping grammars. We also demonstrate that the general versions of jumping grammars characterize the family of recursively enumerable languages. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

scholarly journals A homomorphic characterization of recursively enumerable languages

1985 ◽  
Vol 35 ◽  
pp. 261-269 ◽  
Author(s):  
Sadaki Hirose ◽  
Satoshi Okawa ◽  
Masaaki Yoneda
Keyword(s):  
Recursively Enumerable ◽  
Recursively Enumerable Languages

PROBABILISTIC REWRITING P SYSTEMS

2003 ◽  
Vol 14 (01) ◽  
pp. 157-166 ◽  
Author(s):  
MUTYAM MADHU
Keyword(s):  
P Systems ◽  
Cut Point ◽  
Recursively Enumerable ◽  
The Family ◽  
Rewriting Rules ◽  
Recursively Enumerable Languages ◽  
Selection Of

In this paper we define a variant of P systems, namely, probabilistic rewriting P systems, where the selection of rewriting rules is probabilistic. We show that, with non-zero cut-point, probabilistic rewriting P systems with/without priorities generate only finite languages, but with zero cut/point and without priorities, probabilistic rewriting P systems of degree 1 characterize the family of languages generated by matrix grammars. We also prove that probabilistic rewriting P systems of degree 1 with zero cut-point and priorities characterize recursively enumerable languages.

ON THE LEFTMOST DERVIATION IN MATRIX GRAMMARS

1999 ◽  
Vol 10 (01) ◽  
pp. 61-79 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
HENNING FERNAU ◽  
GHEORGHE PĂUN
Keyword(s):  
Systematic Study ◽  
Regular Language ◽  
Formal Languages ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Leftmost Derivation ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

Matrix grammars are one of the classical topics of formal languages, more specifically, regulated rewriting. Although this type of control on the work of context-free grammars is one of the earliest, matrix grammars still raise interesting questions (not to speak about old open problems in this area). One such class of problems concerns the leftmost derivation (in grammars without appearance checking). The main point of this paper is the systematic study of all possibilities of defining leftmost derivation in matrix grammars. Twelve types of such a restriction are defined, only four of which being discussed in literature. For seven of them, we find a proof of a characterization of recursively enumerable languages (by matrix grammars with arbitrary context-free rules but without appearance checking). Other three cases characterize the recursively enumerable languages modulo a morphism and an intersection with a regular language. In this way, we solve nearly all problems listed as open on page 67 of the monograph [7], which can be seen as the main contribution of this paper. Moreover, we find a characterization of the recursively enumerable languages for matrix grammars with the leftmost restriction defined on classes of a given partition of the nonterminal alphabet.

CELL/SYMBOL COMPLEXITY OF TISSUE P SYSTEMS WITH SYMPORT/ANTIPORT RULES

2006 ◽  
Vol 17 (01) ◽  
pp. 3-25 ◽  
Author(s):  
ARTIOM ALHAZOV ◽  
RUDOLF FREUND ◽  
MARION OSWALD
Keyword(s):  
P Systems ◽  
Computational Power ◽  
Natural Numbers ◽  
Recursively Enumerable Set ◽  
Trade Off ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
A Cell ◽  
Regular Sets ◽  
Number Of Cells

We consider tissue P systems with symport/antiport rules and investigate their computational power when using only a (very) small number of symbols and cells. Even when using only one symbol, we need at most six (seven when allowing only one channel between a cell and the environment) cells to generate any recursively enumerable set of natural numbers. On the other hand, with only one cell we can only generate regular sets when using one channel with the environment, whereas one cell with two channels between the cell and the environment obtains computational completeness with five symbols. Between these extreme cases of one symbol and one cell, respectively, there seems to be a trade-off between the number of cells and the number of symbols. For example, for the case of tissue P systems with two channels between a cell and the environment we show that computational completeness can be obtained with two cells and three symbols as well as with three cells and two symbols, respectively. Moreover, we also show that some variants of tissue P systems characterize the families of finite or regular sets of natural numbers.

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