Encoding Color Sequences in Active Tile Self-Assembly

Constructing patterns is a well-studied problem in both theoretical and experimental self-assembly with much of the work focused on multi-staged assembly. In this paper, we study building 1D patterns in a model of active self assembly: Tile Automata. This is a generalization of the 2-handed assembly model that borrows the concept of state changes from Cellular Automata. In this work we further develop the model by partitioning states as colors and show lower and upper bounds for building patterned assemblies based on an input pattern. Our first two sections utilize recent results to build binary strings along with Turing machine constructions to get Kolmogorov optimal state complexity for building patterns in Tile Automata, and show nearly optimal bounds for one case. For affinity strengthening Tile Automata, where transitions can only increase affinity so there is no detachment, we focus on scaled patterns based on Space Bounded Kolmogorov Complexity. Finally, we examine the affinity strengthening freezing case providing an upper bound based on the minimum context-free grammar. This system utilizes only one dimensional assemblies and has tiles that do not change color

Active Self-Assembly of Simple Units Using an Insertion Primitive

While computer science has given us a framework for determining the complexity and difficulty of solving computational problems, we do not yet have a theoretical framework for knowing what actions, behaviors, and life-like qualities can emerge from a given set of simple modular units. There has been much interest in developing models for programming active self-assembly processes in both the reconfigurable robotics community and the nanotechnology community. With respect to materials science and nanotechnology, the models proposed to date are either not yet implementable with our current understanding of synthetic chemistry or those that are implementable are limited to a set of features that do not capture the power of active components. Prior implementable models of molecular assembly only considered the passive behaviors of attaching and detaching from a complex. Inspired by the algorithmic tile assembly model [Winfree, 1996] and the graph grammar assembly model [Klavins et al., 2004], we describe a formal model for studying the complexity of self-assembled structures with active molecular components. In particular, we add an insertion primitive and we show a direct mapping of our model to a molecular implementation using DNA. We show that the expressive power of this language is stronger than regular languages, but at most as strong as context free grammars. Here, we explore the trade-off between the complexity of the system (in terms of the number of unit types), and the behavior of the system and speed of its assembly. We find that we can grow a line of any given length n in expected time O(log^3 n) using O(log^2 n) monomers. If we grow a line with k insertion rules, either the expected final length is infinite or the expected length at time t is at most (2t+2)^k^2, which is polynomial in t

On the relationship between indexed grammars and logic programs

AbstractThis article provides detailed constructions demonstrating that the class of indexed grammars introduced as a simple extension of context-free grammars has essentially the same expressive power as the class of logic programs with unary predicates and functions and exactly one variable symbol.Some additional considerations are concerned with parsing procedures

Applications of Evolutionary Algorithms in Formal Languages

Starting from the model proposed by means of Grammatical Evolution, we extend the applicability of the parallel and cooperative searching processes of Evolutionary Algorithms to a new topic: Tree Adjoining Grammar parsing. We evolved derived trees using a string-tree-representation.We also used a linear matching function to compare the yield of a derived tree with a given input. The running tests presented several encouraging results. A post running analysis allowed us to propose several research directions for extending the currently known computational mechanisms in the mildly context sensitive class of languages

A survey of compiler development aids

A theoretical background was established for the compilation process by dividing it into five phases and explaining the concepts and algorithms that underpin each. The five selected phases were lexical analysis, syntax analysis, semantic analysis, optimization, and code generation. Graph theoretical optimization techniques were presented, and approaches to code generation were described for both one-pass and multipass compilation environments. Following the initial tutorial sections, more than 20 tools that were developed to aid in the process of writing compilers were surveyed. Eight of the more recent compiler development aids were selected for special attention - SIMCMP/STAGE2, LANG-PAK, COGENT, XPL, AED, CWIC, LIS, and JOCIT. The impact of compiler development aids were assessed some of their shortcomings and some of the areas of research currently in progress were inspected

Indexing Highly Repetitive String Collections

Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through applications like bioinformatics, the string collections experienced a growth that outperforms Moore's Law and challenges our ability of handling them even in compressed form. It turns out, fortunately, that many of these rapidly growing string collections are highly repetitive, so that their information content is orders of magnitude lower than their plain size. The statistical compression methods used for classical collections, however, are blind to this repetitiveness, and therefore a new set of techniques has been developed in order to properly exploit it. The resulting indexes form a new generation of data structures able to handle the huge repetitive string collections that we are facing. In this survey we cover the algorithmic developments that have led to these data structures. We describe the distinct compression paradigms that have been used to exploit repetitiveness, the fundamental algorithmic ideas that form the base of all the existing indexes, and the various structures that have been proposed, comparing them both in theoretical and practical aspects. We conclude with the current challenges in this fascinating field

Techniques for creating ground-truthed sketch corpora

The problem of recognizing handwritten mathematics notation has been studied for over forty years with little practical success. The poor performance of math recognition systems is due, at least in part, to a lack of realistic data for use in training recognition systems and evaluating their accuracy. In fields for which such data is available, such as face and voice recognition, the data, along with objectively-evaluated recognition contests, has contributed to the rapid advancement of the state of the art. This thesis proposes a method for constructing data corpora not only for hand- written math recognition, but for sketch recognition in general. The method consists of automatically generating template expressions, transcribing these expressions by hand, and automatically labelling them with ground-truth. This approach is motivated by practical considerations and is shown to be more extensible and objective than other potential methods. We introduce a grammar-based approach for the template generation task. In this approach, random derivations in a context-free grammar are controlled so as to generate math expressions for transcription. The generation process may be controlled in terms of expression size and distribution over mathematical semantics. Finally, we present a novel ground-truthing method based on matching terminal symbols in grammar derivations to recognized symbols. The matching is produced by a best-first search through symbol recognition results. Experiments show that this method is highly accurate but rejects many of its inputs

A neural compiler

AbstractThis paper describes a neural compiler. The input of the compiler is a PASCAL Program. The compiler produces a neural network that computes what is specified by the PASCAL program. The compiler generates an intermediate code called cellular code