Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results

The Complexity of Tree Transducer Output Languages

Two complexity results are shown for the output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are context-sensitive, and the class is NP-complete

Extended macro grammars and stack controlled machines

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines

Permutations of context-free, ET0L and indexed languages

© 2016 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France. For a language L, we consider its cyclic closure, and more generally the language Ck(L), which consists of all words obtained by partitioning words from L into k factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators Ck. This both sharpens and generalises Brandstädt's result that if L is context-free then Ck(L) is context-sensitive and not context-free in general for k ≥ 3. We also show that the cyclic closure of an indexed language is indexed

Transformational classes of grammars

Given two Chomsky grammars G and \-G, a homomorphism φ from G to \-G is, roughly speaking, a map which assigns to every derivation of G a derivation of \-G in such a manner that φ is uniquely determined by its restriction to the set of productions of G. Two grammars are contained in the same transformational class, if the one can be transformed into the other by a sequence of homomorphisms. If two grammars are related in such a manner, then there are two relations, one concerning the words of the languages generated and the other regarding the derivations of these words. We establish several classifications of context-free grammars in transformational classes which are recursively solvable

The immediacy of the artist's mark in shape computation : from visualization to representation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2006.Includes bibliographical references (leaves 105-109).Approaches to shape computation and algorithmic art-making within the fields of shape grammars and computer graphics still do not consider the immediacy of the artist's mark in drawing and painting. This research examines the canvas, or 2D picture plane, as the expressive and dynamic problem space of the artist who naturally reframes both the problem and the solution with each successive mark. The fluidity of the artist's mark is the most important element in transforming the blank canvas into an image. In this research, I use my own traditionally drawn and painted artwork as the baseline corpus for analysis. From my analysis, I define a nonsymbolic, formal grammar for the synthesis of images in the style of the baseline corpus and develop software prototype "sketches" to support the geometric representation of freehand sketching consistent with mark-making. Curve generation is critical to the expressive marks of the artist. The result of this research is a curvilinear shape grammar that supports both explicit and implicit shape recognition while affording the artist the ability to draw (shape union) and erase (shape difference) computationally.(cont.) I compare the results of the synthesis phase with my traditional sketches showing that it is possible to compute imagery consistent with the evolving style of the artist's own hand. Additionally, the analysis phase of the research supports the supposition that formal algorithmic understanding of one's artistic process has directive and positive influences on the evolution and refinement of the style.by Jacquelyn A. Martino.Ph.D

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure