71 research outputs found
The finite tiling problem is undecidable in the hyperbolic plane
In this paper, we consider the finite tiling problem which was proved
undecidable in the Euclidean plane by Jarkko Kari in 1994. Here, we prove that
the same problem for the hyperbolic plane is also undecidable
A weakly universal cellular automaton in the pentagrid with five states
In this paper, we construct a cellular automaton on the pentagrid which is
planar, weakly universal and which have five states only. This result much
improves the best result which was with nine statesComment: 23 pages, 21 figure
Array P Systems and t−Communication
The two areas of grammar systems and P systems, which have provided interesting computational models in the study of formal string language theory have been in the recent past
effectively linked in [4] by incorporating into P systems, a communication mode called t−mode of cooperating distributed grammar systems. On the other hand cooperating array grammar systems [5]and array P systems [1] have been developed in the context of two-dimensional picture description. In this paper, motivated by the study of [4], these two systems are studied by linking them through
the t−communication mode, thus bringing out the picture description power of these systems
P Systems with Minimal Left and Right Insertion and Deletion
In this article we investigate the operations of insertion and deletion performed
at the ends of a string. We show that using these operations in a P systems
framework (which corresponds to using specific variants of graph control), computational
completeness can even be achieved with the operations of left and right insertion and
deletion of only one symbol
On insertion-deletion systems over relational words
We introduce a new notion of a relational word as a finite totally ordered
set of positions endowed with three binary relations that describe which
positions are labeled by equal data, by unequal data and those having an
undefined relation between their labels. We define the operations of insertion
and deletion on relational words generalizing corresponding operations on
strings. We prove that the transitive and reflexive closure of these operations
has a decidable membership problem for the case of short insertion-deletion
rules (of size two/three and three/two). At the same time, we show that in the
general case such systems can produce a coding of any recursively enumerable
language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure
Small Universal Accepting Networks of Evolutionary Processors with Filtered Connections
In this paper, we present some results regarding the size complexity of
Accepting Networks of Evolutionary Processors with Filtered Connections
(ANEPFCs). We show that there are universal ANEPFCs of size 10, by devising a
method for simulating 2-Tag Systems. This result significantly improves the
known upper bound for the size of universal ANEPFCs which is 18.
We also propose a new, computationally and descriptionally efficient
simulation of nondeterministic Turing machines by ANEPFCs. More precisely, we
describe (informally, due to space limitations) how ANEPFCs with 16 nodes can
simulate in O(f(n)) time any nondeterministic Turing machine of time complexity
f(n). Thus the known upper bound for the number of nodes in a network
simulating an arbitrary Turing machine is decreased from 26 to 16
Complex dynamics of elementary cellular automata emerging from chaotic rules
We show techniques of analyzing complex dynamics of cellular automata (CA)
with chaotic behaviour. CA are well known computational substrates for studying
emergent collective behaviour, complexity, randomness and interaction between
order and chaotic systems. A number of attempts have been made to classify CA
functions on their space-time dynamics and to predict behaviour of any given
function. Examples include mechanical computation, \lambda{} and Z-parameters,
mean field theory, differential equations and number conserving features. We
aim to classify CA based on their behaviour when they act in a historical mode,
i.e. as CA with memory. We demonstrate that cell-state transition rules
enriched with memory quickly transform a chaotic system converging to a complex
global behaviour from almost any initial condition. Thus just in few steps we
can select chaotic rules without exhaustive computational experiments or
recurring to additional parameters. We provide analysis of well-known chaotic
functions in one-dimensional CA, and decompose dynamics of the automata using
majority memory exploring glider dynamics and reactions
Solving 2D-pattern matching with networks of picture processors
We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts simultaneously all subpictures of the same size from the input picture and sends them to the second subnetwork. The second subnetwork checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterwards, we present a solution based on networks containing both evolutionary and hiding processors running in O(n+m+kl+k) computational (processing and communication) steps, where the input picture and the pattern are of size (n,m) and (k,l), respectively
Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants
Abstract geometrical computation can solve hard combinatorial problems
efficiently: we showed previously how Q-SAT can be solved in bounded space and
time using instance-specific signal machines and fractal parallelization. In
this article, we propose an approach for constructing a particular generic
machine for the same task. This machine deploies the Map/Reduce paradigm over a
fractal structure. Moreover our approach is modular: the machine is constructed
by combining modules. In this manner, we can easily create generic machines for
solving satifiability variants, such as SAT, #SAT, MAX-SAT
An Approach to the Bio-Inspired Control of Self-reconfigurable Robots
Self-reconfigurable robots are robots built by modules which
can move in relationship to each other. This ability of changing its physical
form provides the robots a high level of adaptability and robustness.
Given an initial configuration and a goal configuration of the robot, the
problem of self-regulation consists on finding a sequence of module moves
that will reconfigure the robot from the initial configuration to the goal
configuration. In this paper, we use a bio-inspired method for studying
this problem which combines a cluster-flow locomotion based on cellular
automata together with a decentralized local representation of the
spatial geometry based on membrane computing ideas. A promising 3D
software simulation and a 2D hardware experiment are also presented.National Natural Science Foundation of China No. 6167313
- …