Computational Completeness of Path-Structured Graph-Controlled Insertion-Deletion Systems

2017 ◽  
pp. 89-100 ◽  
Author(s):  
Henning Fernau ◽  
Lakshmanan Kuppusamy ◽  
Indhumathi Raman
Keyword(s):  
Computational Completeness

scholarly journals When catalytic P systems with one catalyst can be computationally complete

2021 ◽  
Author(s):  
Artiom Alhazov ◽  
Rudolf Freund ◽  
Sergiu Ivanov
Keyword(s):  
Computational Complexity ◽  
P Systems ◽  
Membrane Systems ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets

AbstractCatalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining computational completeness even with only one catalyst. In this paper, we show that one catalyst is sufficient for obtaining computational completeness if either catalytic rules have weak priority over non-catalytic rules or else instead of the standard maximally parallel derivation mode, we use the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration.

On the Computational Completeness of Matrix Simple Semi-Conditional Grammars

2021 ◽  
pp. 104688
Author(s):  
Henning Fernau ◽  
Lakshmanan Kuppusamy ◽  
Indhumathi Raman
Keyword(s):  
Computational Completeness

scholarly journals Computational Completeness of Interaction Machines and Turing Machines

10.29007/39jj ◽  
2018 ◽  
Author(s):  
Peter Wegner ◽  
Eugene Eberbach ◽  
Mark Burgin
Keyword(s):  
Computer Science ◽  
Complete Theory ◽  
Simple Computation ◽  
Turing Machines ◽  
Complete Model ◽  
Models Of Computation ◽  
Computational Completeness ◽  
Definition Of

In the paper we prove in a new and simple way that Interactionmachines are more powerful than Turing machines. To do thatwe extend the definition of Interaction machines to multiple interactivecomponents, where each component may perform simple computation.The emerging expressiveness is due to the power of interaction and allowsto accept languages not accepted by Turing machines. The mainresult that Interaction machines can accept arbitrary languages over agiven alphabet sheds a new light to the power of interaction. Despite ofthat we do not claim that Interaction machines are complete. We claimthat a complete theory of computer science cannot exist and especially,Turing machines or Interaction machines cannot be a complete model ofcomputation. However complete models of computation may and shouldbe approximated indefinitely and our contribution presents one of suchattempts.

scholarly journals On the computational completeness of graph-controlled insertion–deletion systems with binary sizes

2017 ◽  
Vol 682 ◽  
pp. 100-121 ◽  
Author(s):  
Henning Fernau ◽  
Lakshmanan Kuppusamy ◽  
Indhumathi Raman
Keyword(s):  
Computational Completeness

Computational completeness of simple semi-conditional insertion–deletion systems of degree (2,1)

2019 ◽  
Vol 18 (3) ◽  
pp. 563-577 ◽  
Author(s):  
Henning Fernau ◽  
Lakshmanan Kuppusamy ◽  
Indhumathi Raman
Keyword(s):  
Computational Completeness

Catalytic and Purely Catalytic P Systems and P Automata: Control Mechanisms for Obtaining Computational Completeness

2015 ◽  
Vol 136 (1-2) ◽  
pp. 59-84 ◽  
Author(s):  
Rudolf Freund ◽  
Marion Oswald ◽  
Gheorghe Păun
Keyword(s):  
P Systems ◽  
Control Mechanisms ◽  
Computational Completeness

OPTIMAL RESULTS FOR THE COMPUTATIONAL COMPLETENESS OF GEMMATING (TISSUE) P SYSTEMS

2005 ◽  
Vol 16 (05) ◽  
pp. 929-942 ◽  
Author(s):  
RUDOLF FREUND ◽  
MARION OSWALD ◽  
ANDREI PĂUN
Keyword(s):  
Theoretical Model ◽  
General Model ◽  
P Systems ◽  
Optimal Result ◽  
Recursively Enumerable Language ◽  
Computational Completeness ◽  
Minimal Weight ◽  
Model Based ◽  
Recursively Enumerable ◽  
Enumerable Language

Gemmating P systems were introduced as a theoretical model based on the biological idea of the gemmation of mobile membranes. In the general model of extended gemmating P systems, strings are modified either by evolution rules in the membranes or while sending them to another membrane. We here consider the restricted variant of extended gemmating P systems with pre-dynamic rules where strings are only modified at the ends while sending them from one membrane to another one. In a series of papers the number of membranes being sufficient for obtaining computational completeness has steadily been decreased. In this paper we now prove the optimal result, i.e., gemmating P systems only using pre-dynamic rules are already computationally complete with three membranes, even in the non-extended case and with the minimal weight of rules possible. Moreover, we also show that for gemmating tissue P systems two cells suffice, and if we allow the environment to be fully involved in the communication of strings, even one cell together with the environment can manage the task to generate any recursively enumerable language.

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.

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