Membrane division, restricted membrane creation and object complexity in P systems

We improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one...

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Autores: Alhazov, Artiom, Freund, Rudolf, Riscos Núñez, Agustín
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2006
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/84929
Acceso en línea:https://hdl.handle.net/11441/84929
https://doi.org/10.1080/00207160601065314
Access Level:acceso abierto
Palabra clave:Membrane division
Restricted membrane creation
Object complexity
P systems
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spelling Membrane division, restricted membrane creation and object complexity in P systemsAlhazov, ArtiomFreund, RudolfRiscos Núñez, AgustínMembrane divisionRestricted membrane creationObject complexityP systemsWe improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one object of the same kind.We showhere that they generate all recursively enumerable languages, and that two membrane labels are sufficient (the same result holds for accepting all recursively enumerable vectors of non-negative integers). Moreover, at most two objects are present inside the system at any time in the generative case.We then prove that 10 + msymbols are sufficient to generate any recursively enumerable language over m symbols. P systems with active membranes without polarizations are known to generate all recursively enumerable sets of vectors of non-negative integers. We show that they generate all recursively enumerable languages; four starting membranes with three labels or seven starting membranes with two labels are sufficient. P systems with active membranes and two polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative integers, using only rules of rewriting and sending objects out.We show that accepting can be done by deterministic systems. Finally, we show that P systems with restricted membrane creation (the newly created membrane can only be of the same kind as the parent one) generate at least matrix languages, even when having at most one object in the configuration (except the environment). We conclude by presenting a summary of the main results obtained in this paper and a list of open questions.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-01Taylor and FrancisCiencias de la Computación e Inteligencia ArtificialTIC193: Computación Natural2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/84929https://doi.org/10.1080/00207160601065314reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésInternational Journal of Computer Mathematics, 83 (7), 529-547.TIC2002-04220-C03-01https://www.tandfonline.com/doi/abs/10.1080/00207160601065314info:eu-repo/semantics/openAccessoai:idus.us.es:11441/849292026-06-17T12:51:07Z
dc.title.none.fl_str_mv Membrane division, restricted membrane creation and object complexity in P systems
title Membrane division, restricted membrane creation and object complexity in P systems
spellingShingle Membrane division, restricted membrane creation and object complexity in P systems
Alhazov, Artiom
Membrane division
Restricted membrane creation
Object complexity
P systems
title_short Membrane division, restricted membrane creation and object complexity in P systems
title_full Membrane division, restricted membrane creation and object complexity in P systems
title_fullStr Membrane division, restricted membrane creation and object complexity in P systems
title_full_unstemmed Membrane division, restricted membrane creation and object complexity in P systems
title_sort Membrane division, restricted membrane creation and object complexity in P systems
dc.creator.none.fl_str_mv Alhazov, Artiom
Freund, Rudolf
Riscos Núñez, Agustín
author Alhazov, Artiom
author_facet Alhazov, Artiom
Freund, Rudolf
Riscos Núñez, Agustín
author_role author
author2 Freund, Rudolf
Riscos Núñez, Agustín
author2_role author
author
dc.contributor.none.fl_str_mv Ciencias de la Computación e Inteligencia Artificial
TIC193: Computación Natural
dc.subject.none.fl_str_mv Membrane division
Restricted membrane creation
Object complexity
P systems
topic Membrane division
Restricted membrane creation
Object complexity
P systems
description We improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one object of the same kind.We showhere that they generate all recursively enumerable languages, and that two membrane labels are sufficient (the same result holds for accepting all recursively enumerable vectors of non-negative integers). Moreover, at most two objects are present inside the system at any time in the generative case.We then prove that 10 + msymbols are sufficient to generate any recursively enumerable language over m symbols. P systems with active membranes without polarizations are known to generate all recursively enumerable sets of vectors of non-negative integers. We show that they generate all recursively enumerable languages; four starting membranes with three labels or seven starting membranes with two labels are sufficient. P systems with active membranes and two polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative integers, using only rules of rewriting and sending objects out.We show that accepting can be done by deterministic systems. Finally, we show that P systems with restricted membrane creation (the newly created membrane can only be of the same kind as the parent one) generate at least matrix languages, even when having at most one object in the configuration (except the environment). We conclude by presenting a summary of the main results obtained in this paper and a list of open questions.
publishDate 2006
dc.date.none.fl_str_mv 2006
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/84929
https://doi.org/10.1080/00207160601065314
url https://hdl.handle.net/11441/84929
https://doi.org/10.1080/00207160601065314
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv International Journal of Computer Mathematics, 83 (7), 529-547.
TIC2002-04220-C03-01
https://www.tandfonline.com/doi/abs/10.1080/00207160601065314
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor and Francis
publisher.none.fl_str_mv Taylor and Francis
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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