483 research outputs found
Measuring Communication in Parallel Communicating Finite Automata
Systems of deterministic finite automata communicating by sending their
states upon request are investigated, when the amount of communication is
restricted. The computational power and decidability properties are studied for
the case of returning centralized systems, when the number of necessary
communications during the computations of the system is bounded by a function
depending on the length of the input. It is proved that an infinite hierarchy
of language families exists, depending on the number of messages sent during
their most economical recognitions. Moreover, several properties are shown to
be not semi-decidable for the systems under consideration.Comment: In Proceedings AFL 2014, arXiv:1405.527
Computing with cells: membrane systems - some complexity issues.
Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism
Completeness Results for Parameterized Space Classes
The parameterized complexity of a problem is considered "settled" once it has
been shown to lie in FPT or to be complete for a class in the W-hierarchy or a
similar parameterized hierarchy. Several natural parameterized problems have,
however, resisted such a classification. At least in some cases, the reason is
that upper and lower bounds for their parameterized space complexity have
recently been obtained that rule out completeness results for parameterized
time classes. In this paper, we make progress in this direction by proving that
the associative generability problem and the longest common subsequence problem
are complete for parameterized space classes. These classes are defined in
terms of different forms of bounded nondeterminism and in terms of simultaneous
time--space bounds. As a technical tool we introduce a "union operation" that
translates between problems complete for classical complexity classes and for
W-classes.Comment: IPEC 201
On the Equivalence of Cellular Automata and the Tile Assembly Model
In this paper, we explore relationships between two models of systems which
are governed by only the local interactions of large collections of simple
components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM).
While sharing several similarities, the models have fundamental differences,
most notably the dynamic nature of CA (in which every cell location is allowed
to change state an infinite number of times) versus the static nature of the
aTAM (in which tiles are static components that can never change or be removed
once they attach to a growing assembly). We work with 2-dimensional systems in
both models, and for our results we first define what it means for CA systems
to simulate aTAM systems, and then for aTAM systems to simulate CA systems. We
use notions of simulate which are similar to those used in the study of
intrinsic universality since they are in some sense strict, but also
intuitively natural notions of simulation. We then demonstrate a particular
nondeterministic CA which can be configured so that it can simulate any
arbitrary aTAM system, and finally an aTAM tile set which can be configured so
that it can be used to simulate any arbitrary nondeterministic CA system which
begins with a finite initial configuration.Comment: In Proceedings MCU 2013, arXiv:1309.104
Transductions Computed by One-Dimensional Cellular Automata
Cellular automata are investigated towards their ability to compute
transductions, that is, to transform inputs into outputs. The families of
transductions computed are classified with regard to the time allowed to
process the input and to compute the output. Since there is a particular
interest in fast transductions, we mainly focus on the time complexities real
time and linear time. We first investigate the computational capabilities of
cellular automaton transducers by comparing them to iterative array
transducers, that is, we compare parallel input/output mode to sequential
input/output mode of massively parallel machines. By direct simulations, it
turns out that the parallel mode is not weaker than the sequential one.
Moreover, with regard to certain time complexities cellular automaton
transducers are even more powerful than iterative arrays. In the second part of
the paper, the model in question is compared with the sequential devices
single-valued finite state transducers and deterministic pushdown transducers.
It turns out that both models can be simulated by cellular automaton
transducers faster than by iterative array transducers.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Rice-Like Theorems for Automata Networks
International audienceWe prove general complexity lower bounds on automata networks, in the style of Rice's theorem, but in the computable world. Our main result is that testing any fixed first-order property on the dynamics of an automata network is either trivial, or NP-hard, or coNP-hard. Moreover, there exist such properties that are arbitrarily high in the polynomial-time hierarchy. We also prove that testing a first-order property given as input on an automata network (also part of the input) is PSPACE-hard. Besides, we show that, under a natural effectiveness condition, any nontrivial property of the limit set of a nondeterministic network is PSPACE-hard. We also show that it is PSPACE-hard to separate deterministic networks with a very high and a very low number of limit configurations; however, the problem of deciding whether the number of limit configurations is maximal up to a polynomial quantity belongs to the polynomial-time hierarchy
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
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