Grammars with valuations — a discrete model for self-organization of biopolymers

AbstractWe define a new type of formal grammars where the derivation process is regulated by a certain function which evaluates the words. These grammars can be regarded as a model for the molecular replication process with selective character. We locate the associated family of languages in the Chomsky hierarchy, prove some closure properties, and solve some decision problems which are of interest in formal language theory and in biophysics

Accepting Hybrid Networks of Evolutionary Processors with Special Topologies and Small Communication

Starting from the fact that complete Accepting Hybrid Networks of Evolutionary Processors allow much communication between the nodes and are far from network structures used in practice, we propose in this paper three network topologies that restrict the communication: star networks, ring networks, and grid networks. We show that ring-AHNEPs can simulate 2-tag systems, thus we deduce the existence of a universal ring-AHNEP. For star networks or grid networks, we show a more general result; that is, each recursively enumerable language can be accepted efficiently by a star- or grid-AHNEP. We also present bounds for the size of these star and grid networks. As a consequence we get that each recursively enumerable can be accepted by networks with at most 13 communication channels and by networks where each node communicates with at most three other nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Conditional Lindenmayer systems with subregular conditions : the extended case

We study the generative power of extended conditional Lindenmayer systems where the conditions are finite, monoidal, combinational, definite, nilpotent, strictly locally (k)-testable, commutative, circular, suffix-closed, starfree, and union-free regular languages. The results correspond to those obtained for conditional context-free languages

Petri net controlled grammars with a bounded number of additional places

A context-free grammar and its derivations can be described by a Petri net, called a context-free Petri net, whose places and transitions correspond to the nonterminals and the production rules of the grammar, respectively, and tokens are separate instances of the nonterminals in a sentential form. Therefore , the control of the derivations in a context-free grammar can be implemented by adding some features to the associated cf Petri net. The addition of new places and new arcs from/to these new places to/from transitions of the net leads grammars controlled by k-Petri nets, i.e., Petri nets with additional k places. In the paper we investigate the generative power and give closure properties of the families of languages generated by such Petri net controlled grammars, in particular, we show that these families form an infinite hierarchy with respect to the numbers of additional places

P systems with communication based on concentration

We consider a variant of P systems where the communication of objects is controlled by the "concentration" of these objects: after each evolution step, the objects are redistributed among the regions of the system in such a way that each region contains the same number of copies of each object (plus/minus one, when the number of objects is not divisible by the number of regions). We show that P systems of this form, with only one flip-flop catalyst but without using other control ingredients, can generate the Parikh images of all matrix languages. When an unbounded number of catalysts is available, a characterization of recursively enumerable sets of vectors of natural numbers is obtained (by systems with only one membrane)