1,819 research outputs found
Scale-invariant cellular automata and self-similar Petri nets
Two novel computing models based on an infinite tessellation of space-time
are introduced. They consist of recursively coupled primitive building blocks.
The first model is a scale-invariant generalization of cellular automata,
whereas the second one utilizes self-similar Petri nets. Both models are
capable of hypercomputations and can, for instance, "solve" the halting problem
for Turing machines. These two models are closely related, as they exhibit a
step-by-step equivalence for finite computations. On the other hand, they
differ greatly for computations that involve an infinite number of building
blocks: the first one shows indeterministic behavior whereas the second one
halts. Both models are capable of challenging our understanding of
computability, causality, and space-time.Comment: 35 pages, 5 figure
Bulking II: Classifications of Cellular Automata
This paper is the second part of a series of two papers dealing with bulking:
a way to define quasi-order on cellular automata by comparing space-time
diagrams up to rescaling. In the present paper, we introduce three notions of
simulation between cellular automata and study the quasi-order structures
induced by these simulation relations on the whole set of cellular automata.
Various aspects of these quasi-orders are considered (induced equivalence
relations, maximum elements, induced orders, etc) providing several formal
tools allowing to classify cellular automata
Revisiting Membership Problems in Subclasses of Rational Relations
We revisit the membership problem for subclasses of rational relations over
finite and infinite words: Given a relation R in a class C_2, does R belong to
a smaller class C_1? The subclasses of rational relations that we consider are
formed by the deterministic rational relations, synchronous (also called
automatic or regular) relations, and recognizable relations. For almost all
versions of the membership problem, determining the precise complexity or even
decidability has remained an open problem for almost two decades. In this
paper, we provide improved complexity and new decidability results. (i) Testing
whether a synchronous relation over infinite words is recognizable is
NL-complete (PSPACE-complete) if the relation is given by a deterministic
(nondeterministic) omega-automaton. This fully settles the complexity of this
recognizability problem, matching the complexity of the same problem over
finite words. (ii) Testing whether a deterministic rational binary relation is
recognizable is decidable in polynomial time, which improves a previously known
double exponential time upper bound. For relations of higher arity, we present
a randomized exponential time algorithm. (iii) We provide the first algorithm
to decide whether a deterministic rational relation is synchronous. For binary
relations the algorithm even runs in polynomial time
Bounded Counter Languages
We show that deterministic finite automata equipped with two-way heads
are equivalent to deterministic machines with a single two-way input head and
linearly bounded counters if the accepted language is strictly bounded,
i.e., a subset of for a fixed sequence of symbols . Then we investigate linear speed-up for counter machines. Lower
and upper time bounds for concrete recognition problems are shown, implying
that in general linear speed-up does not hold for counter machines. For bounded
languages we develop a technique for speeding up computations by any constant
factor at the expense of adding a fixed number of counters
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