Four-nonterminal scattered context grammars characterize the family of recursively enumerable languages

1997 ◽  
Vol 63 (1-2) ◽  
pp. 67-83 ◽  
Author(s):  
Alexander Meduna
Keyword(s):  
Recursively Enumerable ◽  
The Family ◽  
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.

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.

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.

COMPUTING WITH MEMBRANES (P SYSTEMS): A VARIANT

2000 ◽  
Vol 11 (01) ◽  
pp. 167-181 ◽  
Author(s):  
GHEORGHE PĂUN
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Pass Through ◽  
The One ◽  
Priority Relation ◽  
Recursively Enumerable Languages ◽  
Biochemical Features ◽  
Computing Models

Membrane Computing is a recently introduced area of Molecular Computing, where a computation takes place in a membrane structure where multisets of objects evolve according to given rules (they can also pass through membranes). The obtained computing models were called P systems. In basic variants of P systems, the use of objects evolution rules is regulated by a given priority relation; moreover, each membrane has a label and one can send objects to precise membranes, identified by their labels. We propose here a variant where we get rid of both there rather artificial (non-biochemical) features. Instead, we add to membranes and to objects an "electrical charge" and the objects are passed through membranes according to their charge. We prove that such systems are able to characterize the one-letter recursively enumerable languages (equivalently, the recursively enumerable sets of natural numbers), providing that an extra feature is considered: the membranes can be made thicker or thinner (also dissolved) and the communication through a membrane is possible only when its thickness is equal to 1. Several open problems are formulated.

scholarly journals Representing recursively enumerable languages by iterated deletion

2004 ◽  
Vol 314 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Michael Domaratzki ◽  
Alexander Okhotin
Keyword(s):  
Recursively Enumerable ◽  
Recursively Enumerable Languages

Probabilistic Semi–Simple Splicing System and Its Characteristics

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Mathuri Selvarajoo ◽  
Fong Wan Heng ◽  
Nor Haniza Sarmin ◽  
Sherzod Turaev
Keyword(s):  
Regular Languages ◽  
Computational Power ◽  
Dna Molecules ◽  
Finite Sets ◽  
Generative Power ◽  
Recursively Enumerable ◽  
Splicing Systems ◽  
Recursively Enumerable Languages

The concept of splicing system was first introduced by Head in 1987. This model has been introduced to investigate the recombinant behavior of DNA molecules. Splicing systems with finite sets of axioms only generate regular languages. Hence, different restrictions have been considered to increase the computational power up to the recursively enumerable languages. Recently, probabilistic splicing systems have been introduced where probabilities are initially associated with the axioms, and the probability of a generated string is computed by multiplying the probabilities of all occurrences of the initial strings in the computation of the string. In this paper, some properties of probabilistic semi-simple splicing systems, which are special types of probabilistic splicing systems, are investigated. We prove that probabilistic semi-simple splicing systems can also increase the generative power of the generated languages.

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