On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations

The new digital economy has renewed interest in how digital agents can innovate. This follows the legacy of John von Neumann dynamical systems theory on complex biological systems as computation. The Gödel-Turing-Post (GTP) logic is shown to be necessary to generate innovation based structure changing Type 4 dynamics of the Wolfram-Chomsky schema. Two syntactic procedures of GTP logic permit digital agents to exit from listable sets of digital technologies to produce novelty and surprises. The first is meta-analyses or offline simulations. The second is a fixed point with a two place encoding of negation or opposition, referred to as the Gödel sentence. It is postulated that in phenomena ranging from the genome to human proteanism, the Gödel sentence is a ubiquitous syntactic construction without which escape from hostile agents qua the Liar is impossible and digital agents become entrained within fixed repertoires. The only recursive best response function of a 2-person adversarial game that can implement strategic innovation in lock-step formation of an arms race is the productive function of the Emil Post [58] set theoretic proof of the Gödel incompleteness result. This overturns the view of game theorists that surprise and innovation cannot be a Nash equilibrium of a game

A Bio-inspired Model of Picture Array Generating P System with Restricted Insertion Rules

In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating $P$ system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array $P$ system

Can a Computationally Creative System Create Itself? Creative Artefacts and Creative Processes

This paper begins by briefly looking at two of the dominant perspectives on computational creativity; focusing on the creative artefacts and the creative processes respectively. We briefly describe two projects; one focused on (artistic) creative artefacts the other on a (scientific) creative process, to highlight some similarities and differences in approach. We then look at a 2- dimensional model of Learning Objectives that uses independent axes of knowledge and (cognitive) processes. This educational framework is then used to cast artefact and process perspectives into a common framework, opening up new possibilities for discussing and comparing creativity between them. Finally, arising from our model of creative processes, we propose a new and broad 4-level hierarchy of computational creativity, which asserts that the highest level of computational creativity involves processes whose creativity is comparable to that of the originating process itself

Can a Computationally Creative System Create Itself? Creative Artefacts and Creative Processes

This paper begins by briefly looking at two of the dominant perspectives on computational creativity; focusing on the creative artefacts and the creative processes respectively. We briefly describe two projects; one focused on (artistic) creative artefacts the other on a (scientific) creative process, to highlight some similarities and differences in approach. We then look at a 2- dimensional model of Learning Objectives that uses independent axes of knowledge and (cognitive) processes. This educational framework is then used to cast artefact and process perspectives into a common framework, opening up new possibilities for discussing and comparing creativity between them. Finally, arising from our model of creative processes, we propose a new and broad 4-level hierarchy of computational creativity, which asserts that the highest level of computational creativity involves processes whose creativity is comparable to that of the originating process itself

Mapping boundaries of generative systems for design synthesis

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2007.Page 123 blank.Includes bibliographical references (p. 121-122).Architects have been experimenting with generative systems for design without a clear reference or theory of what, why or how to deal with such systems. In this thesis I argue for three points. The first is that generative systems in architecture are implemented at a skin-deep level as they are only used to synthesize form within confined domains. The second is that such systems can be only implemented if a design formalism is defined. The third is that generative systems can be deeper integrated within a design process if they were coupled with performance-based evaluation methods. These arguments are discussed in four chapters: 1- Introduction: a panoramic view of generative systems in architecture and in. computing mapping their occurrences and implementations. 2- Generative Systems for Design: highlights on integrating generative systems in architecture design processes; and discussions on six generative systems including: Algorithmic, Parametrics, L-systems, Cellular Automata, Fractals and Shape Grammars. 3- Provisional taxonomy: A summery table of systems properties and a classification of generative systems properties as discussed in the previous chapter 4- Conclusion: comments and explanations on why such systems are simplicity implemented within design.by Maher El-Khaldi.S.M

Recursion in cognition: a computational investigation into the representation and processing of language

La recursividad entendida como auto-referencia se puede aplicar a varios constructos de las ciencias cognitivas, como las definiciones teóricas, los procedimientos mecánicos, los procesos de cálculo (sean éstos abstractos o concretos) o las estructuras. La recursividad es una propiedad central tanto del procedimiento mecánico que subyace a la facultad del lenguaje como de las estructuras que esta facultad genera. Sin embargo, tanto las derivaciones sintácticas de la gramática, que constituyen un proceso computacional abstracto, como las estrategias de procesamiento del parser, que son un proceso en tiempo real, proceden de forma iterativa, lo cual sugiere que la especificación recursiva de un algoritmo se implementa de forma iterativa. Además, la combinación de la recursividad con las unidades léxicas y las imposiciones de los interfaces con los que la facultad del lenguaje interactúa resulta en un conjunto de estructuras sui generis que no tienen parangón en otros dominios cognitivos.Recursion qua self-reference applies to various constructs within the cognitive sciences, such as theoretical definitions, mechanical procedures (or algorithms), (abstract or real-time) computational processes and structures. Recursion is an intrinsic property of both the mechanical procedure underlying the language faculty and the structures this faculty generates. However, the recursive nature of the generated structures and the recursive character of the processes need to be kept distinct, their study meriting individual treatment. In fact, the nature of both the syntactic derivations of the grammar (an abstract computational process) and the processing strategies of the parser (a real-time process) are iterative, which suggests that recursively-defined algorithms are implemented iteratively in linguistic cognition. Furthermore, the combination of recursion, lexical items and the impositions of the interfaces the language faculty interacts with results in a sui generis set of structures with which other domains of the mind bear the most superficial of relations