2,698 research outputs found
Randomization in Non-Uniform Finite Automata
The non-uniform version of Turing machines with an extra advice input tape that depends on the length of the input but not the input itself is a well-studied model in complexity theory. We investigate the same notion of non-uniformity in weaker models, namely one-way finite automata. In particular, we are interested in the power of two-sided bounded-error randomization, and how it compares to determinism and non-determinism. We show that for unlimited advice, randomization is strictly stronger than determinism, and strictly weaker than non-determinism. However, when the advice is restricted to polynomial length, the landscape changes: the expressive power of determinism and randomization does not change, but the power of non-determinism is reduced to the extent that it becomes incomparable with randomization
Disordered cellular automaton traffic flow model: Phase separated state, density waves and self organized criticality
We suggest a disordered traffic flow model that captures many features of
traffic flow. It is an extension of the Nagel-Schreckenberg (NaSch) stochastic
cellular automata for single line vehicular traffic model. It incorporates
random acceleration and deceleration terms that may be greater than one unit.
Our model leads under its intrinsic dynamics, for high values of braking
probability , to a constant flow at intermediate densities without
introducing any spatial inhomogeneities. For a system of fast drivers ,
the model exhibits a density wave behavior that was observed in car following
models with optimal velocity. The gap of the disordered model we present
exhibits, for high values of and random deceleration, at a critical
density, a power law distribution which is a hall mark of a self organized
criticality phenomena.Comment: 23 pages, 14 figure
Topology regulates pattern formation capacity of binary cellular automata on graphs
We study the effect of topology variation on the dynamic behavior of a system
with local update rules. We implement one-dimensional binary cellular automata
on graphs with various topologies by formulating two sets of degree-dependent
rules, each containing a single parameter. We observe that changes in graph
topology induce transitions between different dynamic domains (Wolfram classes)
without a formal change in the update rule. Along with topological variations,
we study the pattern formation capacities of regular, random, small-world and
scale-free graphs. Pattern formation capacity is quantified in terms of two
entropy measures, which for standard cellular automata allow a qualitative
distinction between the four Wolfram classes. A mean-field model explains the
dynamic behavior of random graphs. Implications for our understanding of
information transport through complex, network-based systems are discussed.Comment: 16 text pages, 13 figures. To be published in Physica
Inkdots as advice for finite automata
We examine inkdots placed on the input string as a way of providing advice to
finite automata, and establish the relations between this model and the
previously studied models of advised finite automata. The existence of an
infinite hierarchy of classes of languages that can be recognized with the help
of increasing numbers of inkdots as advice is shown. The effects of different
forms of advice on the succinctness of the advised machines are examined. We
also study randomly placed inkdots as advice to probabilistic finite automata,
and demonstrate the superiority of this model over its deterministic version.
Even very slowly growing amounts of space can become a resource of meaningful
use if the underlying advised model is extended with access to secondary
memory, while it is famously known that such small amounts of space are not
useful for unadvised one-way Turing machines.Comment: 14 page
Superiority of one-way and realtime quantum machines and new directions
In automata theory, the quantum computation has been widely examined for
finite state machines, known as quantum finite automata (QFAs), and less
attention has been given to the QFAs augmented with counters or stacks.
Moreover, to our knowledge, there is no result related to QFAs having more than
one input head. In this paper, we focus on such generalizations of QFAs whose
input head(s) operate(s) in one-way or realtime mode and present many
superiority of them to their classical counterparts. Furthermore, we propose
some open problems and conjectures in order to investigate the power of
quantumness better. We also give some new results on classical computation.Comment: A revised edition with some correction
Cellular Automaton for Realistic Modelling of Landslides
A numerical model is developed for the simulation of debris flow in
landslides over a complex three dimensional topography. The model is based on a
lattice, in which debris can be transferred among nearest neighbors according
to established empirical relationships for granular flows. The model is then
validated by comparing a simulation with reported field data. Our model is in
fact a realistic elaboration of simpler ``sandpile automata'', which have in
recent years been studied as supposedly paradigmatic of ``self-organized
criticality''.
Statistics and scaling properties of the simulation are examined, and show
that the model has an intermittent behavior.Comment: Revised version (gramatical and writing style cleanup mainly).
Accepted for publication by Nonlinear Processes in Geophysics. 16 pages, 98Kb
uuencoded compressed dvi file (that's the way life is easiest). Big (6Mb)
postscript figures available upon request from [email protected] /
[email protected]
The Complexity of POMDPs with Long-run Average Objectives
We study the problem of approximation of optimal values in
partially-observable Markov decision processes (POMDPs) with long-run average
objectives. POMDPs are a standard model for dynamic systems with probabilistic
and nondeterministic behavior in uncertain environments. In long-run average
objectives rewards are associated with every transition of the POMDP and the
payoff is the long-run average of the rewards along the executions of the
POMDP. We establish strategy complexity and computational complexity results.
Our main result shows that finite-memory strategies suffice for approximation
of optimal values, and the related decision problem is recursively enumerable
complete
Intrinsic universality and the computational power of self-assembly
This short survey of recent work in tile self-assembly discusses the use of
simulation to classify and separate the computational and expressive power of
self-assembly models. The journey begins with the result that there is a single
universal tile set that, with proper initialization and scaling, simulates any
tile assembly system. This universal tile set exhibits something stronger than
Turing universality: it captures the geometry and dynamics of any simulated
system. From there we find that there is no such tile set in the
noncooperative, or temperature 1, model, proving it weaker than the full tile
assembly model. In the two-handed or hierarchal model, where large assemblies
can bind together on one step, we encounter an infinite set, of infinite
hierarchies, each with strictly increasing simulation power. Towards the end of
our trip, we find one tile to rule them all: a single rotatable flipable
polygonal tile that can simulate any tile assembly system. It seems this could
be the beginning of a much longer journey, so directions for future work are
suggested.Comment: In Proceedings MCU 2013, arXiv:1309.104
Statistical Physics of Vehicular Traffic and Some Related Systems
In the so-called "microscopic" models of vehicular traffic, attention is paid
explicitly to each individual vehicle each of which is represented by a
"particle"; the nature of the "interactions" among these particles is
determined by the way the vehicles influence each others' movement. Therefore,
vehicular traffic, modeled as a system of interacting "particles" driven far
from equilibrium, offers the possibility to study various fundamental aspects
of truly nonequilibrium systems which are of current interest in statistical
physics. Analytical as well as numerical techniques of statistical physics are
being used to study these models to understand rich variety of physical
phenomena exhibited by vehicular traffic. Some of these phenomena, observed in
vehicular traffic under different circumstances, include transitions from one
dynamical phase to another, criticality and self-organized criticality,
metastability and hysteresis, phase-segregation, etc. In this critical review,
written from the perspective of statistical physics, we explain the guiding
principles behind all the main theoretical approaches. But we present detailed
discussions on the results obtained mainly from the so-called
"particle-hopping" models, particularly emphasizing those which have been
formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include
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