Word Blending and Other Formal Models of Bio-operations

As part of ongoing efforts to view biological processes as computations, several formal models of DNA-based processes have been proposed and studied in the formal language literature. In this thesis, we survey some classical formal language word and language operations, as well as several bio-operations, and we propose a new operation inspired by a DNA recombination lab protocol known as Cross-pairing Polymerase Chain Reaction, or XPCR. More precisely, we define and study a word operation called word blending which models a special case of XPCR, where two words x w p and q w y sharing a non-empty overlap part w generate the word x w y. Properties of word blending that we study include closure properties of the Chomsky families of languages under this operation and its iterated version, existence of solution to equations involving this operation, and its state complexity

On external presentations of infinite graphs

The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in particular, for such systems having a finite description, each state of the system is a configuration of some machine. Then most algorithmic approaches rely on the structure of these configurations. Such characterisations are said internal. In order to apply algorithms detecting a structural property (like identifying connected components) one may have first to transform the system in order to fit the description needed for the algorithm. The problem of internal characterisation is that it hides structural properties, and each solution becomes ad hoc relatively to the form of the configurations. On the contrary, external characterisations avoid explicit naming of the vertices. Such characterisation are mostly defined via graph transformations. In this paper we present two kind of external characterisations: deterministic graph rewriting, which in turn characterise regular graphs, deterministic context-free languages, and rational graphs. Inverse substitution from a generator (like the complete binary tree) provides characterisation for prefix-recognizable graphs, the Caucal Hierarchy and rational graphs. We illustrate how these characterisation provide an efficient tool for the representation of infinite state systems

Design patterns for teaching type checking in a compiler construction course

A course in compiler construction seeks to develop an understanding of well-defined fundamental theory and typically involves the production of a language processor. In a graduate degree in software engineering, the development of a compiler contributes significantly to the developer's comprehension of the practical application of theoretical concepts. Different formal notations are commonly used to define type systems, and some of them are used to teach the semantic analysis phase of language processing. In the traditional approach, attribute grammars are probably the most widely used ones. This paper shows how object-oriented design patterns represented in unified modeling language (UML) can be used to both teach type systems and develop the semantic analysis phase of a compiler. The main benefit of this approach is two-fold: better comprehension of theoretical concepts because of the use of notations known by the students (UML diagrams), and improvement of software engineering skills for the development of a complete language processor

Empiricism and Philosophy

Though Quine's argument against the analytic-synthetic distinction is widely disputed, one of the major effects of his argument has been to popularise the belief that there is no sharp distinction between science and philosophy. This thesis begins by distinguishing reductive from holistic empiricism, showing why reductive empiricism is false, refuting the major objections to holistic empiricism and stating the limits on human knowledge it implies. Quine's arguments (and some arguments that have been mistakenly attributed to him) from holism against the analytic-synthetic are considered, and while many of them are found wanting one good argument is presented. Holism does not, however, imply that there is no sharp distinction between science and philosophy, and indeed implies that the distinction between scientific and philosophical disputes is perfectly sharp. The grounds upon which philosophical disputes may be resolved are then sought for and deliniated

Empiricism and Philosophy

Though Quine's argument against the analytic-synthetic distinction is widely disputed, one of the major effects of his argument has been to popularise the belief that there is no sharp distinction between science and philosophy. This thesis begins by distinguishing reductive from holistic empiricism, showing why reductive empiricism is false, refuting the major objections to holistic empiricism and stating the limits on human knowledge it implies. Quine's arguments (and some arguments that have been mistakenly attributed to him) from holism against the analytic-synthetic are considered, and while many of them are found wanting one good argument is presented. Holism does not, however, imply that there is no sharp distinction between science and philosophy, and indeed implies that the distinction between scientific and philosophical disputes is perfectly sharp. The grounds upon which philosophical disputes may be resolved are then sought for and deliniated

DNA Computing: Modelling in Formal Languages and Combinatorics on Words, and Complexity Estimation

DNA computing, an essential area of unconventional computing research, encodes problems using DNA molecules and solves them using biological processes. This thesis contributes to the theoretical research in DNA computing by modelling biological processes as computations and by studying formal language and combinatorics on words concepts motivated by DNA processes. It also contributes to the experimental research in DNA computing by a scaling comparison between DNA computing and other models of computation. First, for theoretical DNA computing research, we propose a new word operation inspired by a DNA wet lab protocol called cross-pairing polymerase chain reaction (XPCR). We define and study a word operation called word blending that models and generalizes an unexpected outcome of XPCR. The input words are uwx and ywv that share a non-empty overlap w, and the output is the word uwv. Closure properties of the Chomsky families of languages under this operation and its iterated version, the existence of a solution to equations involving this operation, and its state complexity are studied. To follow the XPCR experimental requirement closely, a new word operation called conjugate word blending is defined, where the subwords x and y are required to be identical. Closure properties of the Chomsky families of languages under this operation and the XPCR experiments that motivate and implement it are presented. Second, we generalize the sequence of Fibonacci words inspired by biological concepts on DNA. The sequence of Fibonacci words is an infinite sequence of words obtained from two initial letters f(1) = a and f(2)= b, by the recursive definition f(n+2) = f(n+1)*f(n), for all positive integers n, where * denotes word concatenation. After we propose a unified terminology for different types of Fibonacci words and corresponding results in the extensive literature on the topic, we define and explore involutive Fibonacci words motivated by ideas stemming from theoretical studies of DNA computing. The relationship between different involutive Fibonacci words and their borderedness and primitivity are studied. Third, we analyze the practicability of DNA computing experiments since DNA computing and other unconventional computing methods that solve computationally challenging problems often have the limitation that the space of potential solutions grows exponentially with their sizes. For such problems, DNA computing algorithms may achieve a linear time complexity with an exponential space complexity as a trade-off. Using the subset sum problem as the benchmark problem, we present a scaling comparison of the DNA computing (DNA-C) approach with the network biocomputing (NB-C) and the electronic computing (E-C) approaches, where the volume, computing time, and energy required, relative to the input size, are compared. Our analysis shows that E-C uses a tiny volume compared to that required by DNA-C and NB-C, at the cost of the E-C computing time being outperformed first by DNA-C and then by NB-C. In addition, NB-C appears to be more energy efficient than DNA-C for some input sets, and E-C is always an order of magnitude less energy efficient than DNA-C