7 research outputs found
Universalities in cellular automata; a (short) survey
This reading guide aims to provide the reader with an easy access to the study of universality in the field of cellular automata. To fulfill this goal, the approach taken here is organized in three parts: a detailled chronology of seminal papers, a discussion of the definition and main properties of universal cellular automata, and a broad bibliography
Stepping Beyond the Newtonian Paradigm in Biology. Towards an Integrable Model of Life: Accelerating Discovery in the Biological Foundations of Science
The INBIOSA project brings together a group of experts across many disciplines
who believe that science requires a revolutionary transformative
step in order to address many of the vexing challenges presented by the
world. It is INBIOSA’s purpose to enable the focused collaboration of an
interdisciplinary community of original thinkers.
This paper sets out the case for support for this effort. The focus of the
transformative research program proposal is biology-centric. We admit
that biology to date has been more fact-oriented and less theoretical than
physics. However, the key leverageable idea is that careful extension of the
science of living systems can be more effectively applied to some of our
most vexing modern problems than the prevailing scheme, derived from
abstractions in physics. While these have some universal application and
demonstrate computational advantages, they are not theoretically mandated
for the living. A new set of mathematical abstractions derived from biology
can now be similarly extended. This is made possible by leveraging
new formal tools to understand abstraction and enable computability. [The
latter has a much expanded meaning in our context from the one known
and used in computer science and biology today, that is "by rote algorithmic
means", since it is not known if a living system is computable in this
sense (Mossio et al., 2009).] Two major challenges constitute the effort.
The first challenge is to design an original general system of abstractions
within the biological domain. The initial issue is descriptive leading to the
explanatory. There has not yet been a serious formal examination of the
abstractions of the biological domain. What is used today is an amalgam;
much is inherited from physics (via the bridging abstractions of chemistry)
and there are many new abstractions from advances in mathematics (incentivized
by the need for more capable computational analyses). Interspersed
are abstractions, concepts and underlying assumptions “native” to biology
and distinct from the mechanical language of physics and computation as
we know them. A pressing agenda should be to single out the most concrete
and at the same time the most fundamental process-units in biology
and to recruit them into the descriptive domain. Therefore, the first challenge
is to build a coherent formal system of abstractions and operations
that is truly native to living systems.
Nothing will be thrown away, but many common methods will be philosophically
recast, just as in physics relativity subsumed and reinterpreted
Newtonian mechanics.
This step is required because we need a comprehensible, formal system to
apply in many domains. Emphasis should be placed on the distinction between
multi-perspective analysis and synthesis and on what could be the
basic terms or tools needed.
The second challenge is relatively simple: the actual application of this set
of biology-centric ways and means to cross-disciplinary problems. In its
early stages, this will seem to be a “new science”.
This White Paper sets out the case of continuing support of Information
and Communication Technology (ICT) for transformative research in biology
and information processing centered on paradigm changes in the epistemological,
ontological, mathematical and computational bases of the science
of living systems. Today, curiously, living systems cannot be said to
be anything more than dissipative structures organized internally by genetic
information. There is not anything substantially different from abiotic
systems other than the empirical nature of their robustness. We believe that
there are other new and unique properties and patterns comprehensible at
this bio-logical level. The report lays out a fundamental set of approaches
to articulate these properties and patterns, and is composed as follows.
Sections 1 through 4 (preamble, introduction, motivation and major biomathematical
problems) are incipient. Section 5 describes the issues affecting
Integral Biomathics and Section 6 -- the aspects of the Grand Challenge
we face with this project. Section 7 contemplates the effort to
formalize a General Theory of Living Systems (GTLS) from what we have
today. The goal is to have a formal system, equivalent to that which exists
in the physics community. Here we define how to perceive the role of time
in biology. Section 8 describes the initial efforts to apply this general theory
of living systems in many domains, with special emphasis on crossdisciplinary
problems and multiple domains spanning both “hard” and
“soft” sciences. The expected result is a coherent collection of integrated
mathematical techniques. Section 9 discusses the first two test cases, project
proposals, of our approach. They are designed to demonstrate the ability
of our approach to address “wicked problems” which span across physics,
chemistry, biology, societies and societal dynamics. The solutions
require integrated measurable results at multiple levels known as “grand
challenges” to existing methods. Finally, Section 10 adheres to an appeal
for action, advocating the necessity for further long-term support of the
INBIOSA program.
The report is concluded with preliminary non-exclusive list of challenging
research themes to address, as well as required administrative actions. The
efforts described in the ten sections of this White Paper will proceed concurrently.
Collectively, they describe a program that can be managed and
measured as it progresses
Programmation et indécidabilités dans les systèmes complexes
N/AUn système complexe est un système constitué d'un ensemble d'entités quiinteragissent localement, engendrant des comportements globaux, émergeant dusystème, qu'on ne sait pas expliquer à partir du comportement local, connu, desentités qui le constituent. Nos travaux ont pour objet de mieux cerner lesliens entre certaines propriétés des systèmes complexes et le calcul. Parcalcul, il faut entendre l'objet d'étude de l'informatique, c'est-à-dire ledéplacement et la combinaison d'informations. À l'aide d'outils issus del'informatique, l'algorithmique et la programmation dans les systèmes complexessont abordées selon trois points de vue. Une première forme de programmation,dite externe, consiste à développer l'algorithmique qui permet de simuler lessystèmes étudiés. Une seconde forme de programmation, dite interne, consiste àdévelopper l'algorithmique propre à ces systèmes, qui permet de construire desreprésentants de ces systèmes qui exhibent des comportements programmés. Enfin,une troisième forme de programmation, de réduction, consiste à plonger despropriétés calculatoires complexes dans les représentants de ces systèmes pourétablir des résultats d'indécidabilité -- indice d'une grande complexitécalculatoire qui participe à l'explication de la complexité émergente. Afin demener à bien cette étude, les systèmes complexes sont modélisés par desautomates cellulaires. Le modèle des automates cellulaires offre une dualitépertinente pour établir des liens entre complexité des propriétés globales etcalcul. En effet, un automate cellulaire peut être décrit à la fois comme unréseau d'automates, offrant un point de vue familier de l'informatique, etcomme un système dynamique discret, une fonction définie sur un espacetopologique, offrant un point de vue familier de l'étude des systèmesdynamiques discrets.Une première partie de nos travaux concerne l'étude de l'objet automatecellulaire proprement dit. L'observation expérimentale des automatescellulaires distingue, dans la littérature, deux formes de dynamiques complexesdominantes. Certains automates cellulaires présentent une dynamique danslaquelle émergent des structures simples, sortes de particules qui évoluentdans un domaine régulier, se rencontrent lors de brèves collisions, avant degénérer d'autres particules. Cette forme de complexité, dans laquelletransparaît une notion de quanta d'information localisée en interaction, estl'objet de nos études. Un premier champ de nos investigations est d'établir uneclassification algébrique, le groupage, qui tend à rendre compte de ce type decomportement. Cette classification met à jour un type d'automate cellulaireparticulier : les automates cellulaires intrinsèquement universels. Un automatecellulaire intrinsèquement universel est capable de simuler le comportement detout automate cellulaire. C'est l'objet de notre second champ d'investigation.Nous caractérisons cette propriété et démontrons son indécidabilité. Enfin, untroisième champ d'investigation concerne l'algorithmique des automatescellulaires à particules et collisions. Étant donné un ensemble de particuleset de collisions d'un tel automate cellulaire, nous étudions l'ensemble desinteractions possibles et proposons des outils pour une meilleure programmationinterne à l'aide de ces collisions.Une seconde partie de nos travaux concerne la programmation par réduction. Afinde démontrer l'indécidabilité de propriétés dynamiques des automatescellulaires, nous étudions d'une part les problèmes de pavage du plan par desjeux de tuiles finis et d'autre part les problèmes de mortalité et depériodicité dans les systèmes dynamiques discrets à fonction partielle. Cetteétude nous amène à considérer des objets qui possèdent la même dualité entredescription combinatoire et topologique que les automates cellulaires. Unenotion d'apériodicité joue un rôle central dans l'indécidabilité des propriétésde ces objets
Some small self-describing Turing machines
Several small self-describing Turing machines are constructed. The number of instructions varies from 275 to 206, depending on the chosen encoding principles. The previous Thatcher's result (2532 instructions of self-describing machine in Wang's format) is essentially improved