On three variants of rewriting P systems

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Interactive L systems with almost interactionless behaviour

A restricted version of interactive L systems is introduced. A P2L system is called an essentially growing 2L-systems (e-G2L system) if every length-preserving production is interactionless (context-free). It is shown that the deterministic e-G2L systems can be simulated by codings of propagating interactionless systems, and that this is not possible for the nondeterministic version. Some interesting properties of e-GD2L systems are established, the main result being the decidability of the sequence equivalence problem for them

Relationships Between Bounded Languages, Counter Machines, Finite-Index Grammars, Ambiguity, and Commutative Equivalence

It is shown that for every language family that is a trio containing only semilinear languages, all bounded languages in it can be accepted by one-way deterministic reversal-bounded multicounter machines (DCM). This implies that for every semilinear trio (where these properties are effective), it is possible to decide containment, equivalence, and disjointness concerning its bounded languages. A condition is also provided for when the bounded languages in a semilinear trio coincide exactly with those accepted by DCM machines, and it is used to show that many grammar systems of finite index — such as finite-index matrix grammars (Mfin) and finite-index ET0L (ET0Lfin) — have identical bounded languages as DCM. Then connections between ambiguity, counting regularity, and commutative regularity are made, as many machines and grammars that are unambiguous can only generate/accept counting regular or com- mutatively regular languages. Thus, such a system that can generate/accept a non-counting regular or non-commutatively regular language implies the existence of inherently ambiguous languages over that system. In addition, it is shown that every language generated by an unambiguous Mfin has a rational char- acteristic series in commutative variables, and is counting regular. This result plus the connections are used to demonstrate that the grammar systems Mfin and ET0Lfin can generate inherently ambiguous languages (over their grammars), as do several machine models. It is also shown that all bounded languages generated by these two grammar systems (those in any semilinear trio) can be generated unambiguously within the systems. Finally, conditions on Mfin and ET0Lfin languages implying commutative regularity are obtained. In particular, it is shown that every finite-index ED0L language is commutatively regular

A Characterization of ET0L and EDT0L Languages

There exists a PT0L language $L_0$ such that the following holds. A language $L$ is an ET0L language if and only if there exists a mapping $T$ induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that $L = T(L_0)$. There exists an infinite collection of EPDT0L languages $D_{mn}\subseteq\Sigma_{mn}^\star$ ($n\geq m\geq 1$) such that the family EDT0L is characterized in the following way. A language $L$ is an EDT0L language if and only if there exists $n\geq m\geq 1$, a homomorphism $h$ and a regular language $R \subseteq \Sigma_{mn}^\star$ such that $L = h(D_{mn} \cap R)$.\u

Variants of P Systems with Toxic Objects

Toxic objects have been introduced to avoid trap rules, especially in (purely) catalytic P systems. No toxic object is allowed to stay idle during a valid derivation in a P system with toxic objects. In this paper we consider special variants of toxic P systems where the set of toxic objects is prede ned { either by requiring all objects to be toxic or all catalysts to be toxic or all objects except the catalysts to be toxic. With all objects staying inside and being toxic, purely catalytic P systems cannot go beyond the nite sets, neither as generating nor as accepting systems. With allowing the output to be sent to the environment, exactly the regular sets can be generated. With non-cooperative systems with all objects being toxic we can generate exactly the Parikh sets of languages generated by extended Lindenmayer systems. Catalytic P systems with all catalysts being toxic can generate at least PsMAT

The biological and mathematical basis of L systems

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26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband

Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk

Accepting grammars and systems

We investigate several kinds of regulated rewriting (programmed, matrix, with regular control, ordered, and variants thereof) and of parallel rewriting mechanisms (Lindenmayer systems, uniformly limited Lindenmayer systems, limited Lindenmayer systems and scattered context grammars) as accepting devices, in contrast with the usual generating mode. In some cases, accepting mode turns out to be just as powerful as generating mode, e.g. within the grammars of the Chomsky hierarchy, within random context, regular control, L systems, uniformly limited L systems, scattered context. Most of these equivalences can be proved using a metatheorem on so-called context condition grammars. In case of matrix grammars and programmed grammars without appearance checking, a straightforward construction leads to the desired equivalence result. Interestingly, accepting devices are (strictly) more powerful than their generating counterparts in case of ordered grammars, programmed and matrix grammars with appearance checking (even programmed grammarsm with unconditional transfer), and 1lET0L systems. More precisely, if we admit erasing productions, we arrive at new characterizations of the recursivley enumerable languages, and if we do not admit them, we get new characterizations of the context-sensitive languages. Moreover, we supplement the published literature showing: - The emptiness and membership problems are recursivley solvable for generating ordered grammars, even if we admit erasing productions. - Uniformly limited propagating systems can be simulated by programmed grammars without erasing and without appearance checking, hence the emptiness and membership problems are recursively solvable for such systems. - We briefly discuss the degree of nondeterminism and the degree of synchronization for devices with limited parallelism

Mehrfach-limitierte Lindenmayer-Systeme

The theory of L systems originated with the biologist and mathematician Aristide Lindenmayer. His original goal was to provide mathematical models for the simultaneous development of cells in filamentous organisms. Since L systems may be viewed as rewriting systems, their generated languages, i.e., sets of organisms encoded by strings, are also subject to formal language theory, which aims to classify formal languages as well as their generating mechanisms according to various properties, such as generative power, decidability, etc. D. Wätjen introduced and studied k-limited L systems in order to combine the purely sequential mode of rewriting and the purely parallel mode of rewriting in context-free grammars, respectively, L systems. In biology, these systems may be interpreted as organisms, for which the simultaneous growth of cells is restricted by the supply of some resources of food being limited by some finite value k. In this thesis the constraint of a common limit k is relaxed in favor of individual resource limits k(a) for every cell-type a, which yields the new notion of multi-limited L system. The language families generated by such systems are then classified according to their sets of limits k(a). At first, an intuitive approach to the different mechanisms of the L system variants is provided by presenting a method for the graphical interpretation of L systems, the so-called turtle interpretation. Suitable computer programs implementing a turtle interpreter as well as free-programmable simulators for multi-limited, k-limited, and uniformly k-limited L systems, are developed and their source-code is appended. Subsequently, language families generated by multi-limited L systems are compared to each other, to Wätjen's k-limited as well as to non-limited language families, and to the families of the Chomsky Hierarchy. Besides asymptotically comparing the generative power of multi-limited L systems to that of the underlying non-limited L systems, also their closure properties are investigated.Der Biologe und Mathematiker Aristide Lindenmayer begründete die Theorie der L-Systeme. Das ursprüngliche Ziel dieser Theorie ist die Bereitstellung mathematischer Modelle zur Untersuchung des simultanen Zellwachstums fadenartiger Organismen. Da L-Systeme als eine Art von Ersetzungssystemen definiert sind, sind ihre erzeugten Sprachen, d.h. die Mengen der durch Zeichenketten beschriebenen Organismen, ebenfalls Gegenstand der Theorie der formalen Sprachen. Diese Theorie klassifiziert formale Sprachen sowie ihre Erzeugungsmechanismen gemäß ihrer Eigenschaften, wie z.B. Erzeugungsmächtigkeit oder Entscheidbarkeit. Als ein Sprachen-erzeugender Mechanismus, der zwischen der rein sequentiellen Ersetzung kontextfreier Grammatiken und der rein parallelen Ersetzung von L-Systemen liegt, sind k-limitierte L-Systeme von D. Wätjen eingeführt und untersucht worden. In der Biologie können diese Systeme als Organismen interpretiert werden, deren simultanes Zellwachstum beschränkt ist durch individuelle Nahrungsvorräte mit einer einheitlichen endlichen Kapazität k. Die in dieser Arbeit betrachteten mehrfach-limitierten L-Systeme bilden eine Verallgemeinerung der k-limitierten L-Systeme, indem sie für jeden Zelltyp a einen individuellen Nahrungsvorrat mit einer spezifischen Kapazität k(a) anstelle der einheitlichen Kapazität k vorsehen. Diese Arbeit führt mehrfach-limitierte L-Systeme ein und definiert eine geeignete Kategorisierung der von ihnen erzeugten Sprachfamilien anhand der erlaubten Mengen von Limits k(a). Zunächst wird ein intuitiver Zugang zu den verschiedenen Mechanismen der L-System-Varianten ermöglicht, indem eine Methode zur grafischen Interpretation von L-Systemen, die sogenannte Turtle-Interpretation, vorgestellt wird. Hierzu werden geeignete Computer-Programme für einen Turtle-Interpreter sowie für frei programmierbare Simulatoren von mehrfach-limitierten, k-limitierten sowie uniform k-limitierten L-Systemen erstellt und ihr Quell-Code zur Verfügung gestellt. Die von mehrfach-limitierten L-Systemen erzeugten Sprachfamilien werden bzgl. ihrer Inklusionseigenschaften untereinander, mit Wätjens k-limitierten Sprachfamilien, mit den nicht-limitierten Sprachfamilien sowie mit der Chomsky Hierarchie verglichen. Die Erzeugungsmächtigkeit von mehrfach-limitierten L-Systemen wird asymptotisch verglichen mit den jeweils unterliegenden nicht-limitierten L-Systemen. Des weiteren werden die Abschlusseigenschaften der mehrfach-limitierten L-Systeme untersucht