Self-regulating finite automata

This paper introduces and discusses self-regulating finite automata. In essence, these automata regulate the use of their rules by a sequence of rules applied during previous moves. A special attention is paid to turns defined as moves during which a self-regulating finite automaton starts a new self-regulating sequence of moves. Based on the number of turns, the present paper establishes two infinite hierarchies of language families resulting from two variants of these automata. In addition, it demonstrates that these hierarchies coincide with the hierarchies resulting from parallel right linear grammars and right linear simple matrix grammars, so the self-regulating finite automata can be viewed as the automaton counterparts to these grammars. Finally, this paper compares both infinite hierarchies. In addition, as an open problem area, it suggests the discussion of self-regulating pushdown automata and points out that they give rise to no infinite hierarchy analogical to the achieved hierarchies resulting from the self-regulating finite automata

Soft behaviour modelling of user communities

A soft modelling approach for describing behaviour in on-line user communities is introduced in this work. Behaviour models of individual users in dynamic virtual environments have been described in the literature in terms of timed transition automata; they have various drawbacks. Soft multi/agent behaviour automata are defined and proposed to describe multiple user behaviours and to recognise larger classes of user group histories, such as group histories which contain unexpected behaviours. The notion of deviation from the user community model allows defining a soft parsing process which assesses and evaluates the dynamic behaviour of a group of users interacting in virtual environments, such as e-learning and e-business platforms. The soft automaton model can describe virtually infinite sequences of actions due to multiple users and subject to temporal constraints. Soft measures assess a form of distance of observed behaviours by evaluating the amount of temporal deviation, additional or omitted actions contained in an observed history as well as actions performed by unexpected users. The proposed model allows the soft recognition of user group histories also when the observed actions only partially meet the given behaviour model constraints. This approach is more realistic for real-time user community support systems, concerning standard boolean model recognition, when more than one user model is potentially available, and the extent of deviation from community behaviour models can be used as a guide to generate the system support by anticipation, projection and other known techniques. Experiments based on logs from an e-learning platform and plan compilation of the soft multi-agent behaviour automaton show the expressiveness of the proposed model

Self-Replicating Strands that Self-Assemble into User-Specified Meshes

It has been argued that a central objective of nanotechnology is to make products inexpensively, and that self-replication is an effective approach to very low-cost manufacturing. The research presented here is intended to be a step towards this vision. In previous work (JohnnyVon 1.0), we simulated machines that bonded together to form self-replicating strands. There were two types of machines (called types 0 and 1), which enabled strands to encode arbitrary bit strings. However, the information encoded in the strands had no functional role in the simulation. The information was replicated without being interpreted, which was a significant limitation for potential manufacturing applications. In the current work (JohnnyVon 2.0), the information in a strand is interpreted as instructions for assembling a polygonal mesh. There are now four types of machines and the information encoded in a strand determines how it folds. A strand may be in an unfolded state, in which the bonds are straight (although they flex slightly due to virtual forces acting on the machines), or in a folded state, in which the bond angles depend on the types of machines. By choosing the sequence of machine types in a strand, the user can specify a variety of polygonal shapes. A simulation typically begins with an initial unfolded seed strand in a soup of unbonded machines. The seed strand replicates by bonding with free machines in the soup. The child strands fold into the encoded polygonal shape, and then the polygons drift together and bond to form a mesh. We demonstrate that a variety of polygonal meshes can be manufactured in the simulation, by simply changing the sequence of machine types in the seed

Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $\omega(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size

Control of complex networks requires both structure and dynamics

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.Comment: 15 pages, 6 figure

Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), which is encoded by a bitstring. The links of the network connect nodes with complementary and nearly complementary bitstrings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists, otherwise it is empty. There is a continuous influx of new B-lymphocytes of random idiotype from the bone marrow. B-lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors, unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which allow to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table