6,984 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
On equivalence, languages equivalence and minimization of multi-letter and multi-letter measure-many quantum automata
We first show that given a -letter quantum finite automata
and a -letter quantum finite automata over
the same input alphabet , they are equivalent if and only if they are
-equivalent where , , are the
numbers of state in respectively, and . By
applying a method, due to the author, used to deal with the equivalence problem
of {\it measure many one-way quantum finite automata}, we also show that a
-letter measure many quantum finite automaton and a
-letter measure many quantum finite automaton are
equivalent if and only if they are -equivalent
where , , are the numbers of state in respectively,
and .
Next, we study the language equivalence problem of those two kinds of quantum
finite automata. We show that for -letter quantum finite automata, the
non-strict cut-point language equivalence problem is undecidable, i.e., it is
undecidable whether
where
and are -letter quantum finite automata.
Further, we show that both strict and non-strict cut-point language equivalence
problem for -letter measure many quantum finite automata are undecidable.
The direct consequences of the above outcomes are summarized in the paper.
Finally, we comment on existing proofs about the minimization problem of one
way quantum finite automata not only because we have been showing great
interest in this kind of problem, which is very important in classical automata
theory, but also due to that the problem itself, personally, is a challenge.
This problem actually remains open.Comment: 30 pages, conclusion section correcte
Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure
String languages recognizable in (deterministic) log-space are characterized
either by two-way (deterministic) multi-head automata, or following Immerman,
by first-order logic with (deterministic) transitive closure. Here we elaborate
this result, and match the number of heads to the arity of the transitive
closure. More precisely, first-order logic with k-ary deterministic transitive
closure has the same power as deterministic automata walking on their input
with k heads, additionally using a finite set of nested pebbles. This result is
valid for strings, ordered trees, and in general for families of graphs having
a fixed automaton that can be used to traverse the nodes of each of the graphs
in the family. Other examples of such families are grids, toruses, and
rectangular mazes. For nondeterministic automata, the logic is restricted to
positive occurrences of transitive closure.
The special case of k=1 for trees, shows that single-head deterministic
tree-walking automata with nested pebbles are characterized by first-order
logic with unary deterministic transitive closure. This refines our earlier
result that placed these automata between first-order and monadic second-order
logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur
From Models to Simulations
This book analyses the impact computerization has had on contemporary science and explains the origins, technical nature and epistemological consequences of the current decisive interplay between technology and science: an intertwining of formalism, computation, data acquisition, data and visualization and how these factors have led to the spread of simulation models since the 1950s.
Using historical, comparative and interpretative case studies from a range of disciplines, with a particular emphasis on the case of plant studies, the author shows how and why computers, data treatment devices and programming languages have occasioned a gradual but irresistible and massive shift from mathematical models to computer simulations
On the possible Computational Power of the Human Mind
The aim of this paper is to address the question: Can an artificial neural
network (ANN) model be used as a possible characterization of the power of the
human mind? We will discuss what might be the relationship between such a model
and its natural counterpart. A possible characterization of the different power
capabilities of the mind is suggested in terms of the information contained (in
its computational complexity) or achievable by it. Such characterization takes
advantage of recent results based on natural neural networks (NNN) and the
computational power of arbitrary artificial neural networks (ANN). The possible
acceptance of neural networks as the model of the human mind's operation makes
the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of
Liverpool, UK. 23 page
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