On the relationship between the LL(k) and LR(k) grammars

In the literature various proofs of the inclusion of the class of LL(k) grammars into the class of LR(k) grammars can be found. Some of these proofs are not correct, others are informal, semi-formal or contain flaws. Some of them are correct but the proof is less straightforward than demonstrated here

Sublinearly space bounded iterative arrays

Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio

String Diagrammatic Trace Theory

We extend the theory of formal languages in monoidal categories to the multi-sorted, symmetric case, and show how this theory permits a graphical treatment of topics in concurrency. In particular, we show that Mazurkiewicz trace languages are precisely symmetric monoidal languages over monoidal distributed alphabets. We introduce symmetric monoidal automata, which define the class of regular symmetric monoidal languages. Furthermore, we prove that Zielonka's asynchronous automata coincide with symmetric monoidal automata over monoidal distributed alphabets. Finally, we apply the string diagrams for symmetric premonoidal categories to derive serializations of traces.Comment: Paper accepted for MFCS 202

Toward an isomorphic diagram of the Backus-Naur form.

Computer scientists studying formal languages have made use of a variety of representations to both reason, and communicate their ideas to others. Symbolic representations have proved useful for rigorously defining the theoretical objects of the preceding topics; however, research shows that diagrammatic representations are as fundamental to these subjects. Previous research in this domain has typically been interested in studying the semantics that a particular representation is intended to capture. By contrast, this treatise considers the importance of the format of the representations themselves, and how format influences the ability of a person to uncover characteristics, relevant to the problem domain. More specifically, this thesis investigates the established formalisms that have been devised to describe formal languages, and introduces a novel concept, an augmented syntax graph. This graph, an isomorphism of the Backus-Naur form, is shown to have application in visualizing properties that are pertinent to some parsing algorithms

Accepting grammars and systems

We investigate several kinds of regulated rewriting (programmed, matrix, with regular control, ordered, and variants thereof) and of parallel rewriting mechanisms (Lindenmayer systems, uniformly limited Lindenmayer systems, limited Lindenmayer systems and scattered context grammars) as accepting devices, in contrast with the usual generating mode. In some cases, accepting mode turns out to be just as powerful as generating mode, e.g. within the grammars of the Chomsky hierarchy, within random context, regular control, L systems, uniformly limited L systems, scattered context. Most of these equivalences can be proved using a metatheorem on so-called context condition grammars. In case of matrix grammars and programmed grammars without appearance checking, a straightforward construction leads to the desired equivalence result. Interestingly, accepting devices are (strictly) more powerful than their generating counterparts in case of ordered grammars, programmed and matrix grammars with appearance checking (even programmed grammarsm with unconditional transfer), and 1lET0L systems. More precisely, if we admit erasing productions, we arrive at new characterizations of the recursivley enumerable languages, and if we do not admit them, we get new characterizations of the context-sensitive languages. Moreover, we supplement the published literature showing: - The emptiness and membership problems are recursivley solvable for generating ordered grammars, even if we admit erasing productions. - Uniformly limited propagating systems can be simulated by programmed grammars without erasing and without appearance checking, hence the emptiness and membership problems are recursively solvable for such systems. - We briefly discuss the degree of nondeterminism and the degree of synchronization for devices with limited parallelism

A String Diagrammatic Axiomatisation of Finite-State Automata

We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. Moreover, we provide an equational theory that completely axiomatises language equivalence in this new setting. This theory has two notable features. First, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks. Second, the proposed axiomatisation is finitary -- a result which is provably impossible to obtain for the one-dimensional syntax of regular expressions.Comment: Minor corrections, in particular in the proof of completeness (including the ordering of the steps of Brzozowski's algorithm

Towards a Step Semantics for Story-Driven Modelling

Graph Transformation (GraTra) provides a formal, declarative means of specifying model transformation. In practice, GraTra rule applications are often programmed via an additional language with which the order of rule applications can be suitably controlled. Story-Driven Modelling (SDM) is a dialect of programmed GraTra, originally developed as part of the Fujaba CASE tool suite. Using an intuitive, UML-inspired visual syntax, SDM provides usual imperative control flow constructs such as sequences, conditionals and loops that are fairly simple, but whose interaction with individual GraTra rules is nonetheless non-trivial. In this paper, we present the first results of our ongoing work towards providing a formal step semantics for SDM, which focuses on the execution of an SDM specification.Comment: In Proceedings GaM 2016, arXiv:1612.0105

Layout Specification on the Concrete and Abstract Syntax Level of a Diagram Language

A visual language consists of several visual component types, e.g. states or transitions in DFAs. Nowadays, the language itself is usually specified via a meta model. To make a diagram look nice, a layouter is required. This layouter may either operate on the concrete syntax level, i.e., on the visual components, or on the abstract syntax level, i.e., on the model instance. In this paper we present an approach that is capable of specifying a flexible layout on both, the concrete as well as the abstract syntax level of a diagram. The approach uses pattern-based transformations. Besides structured editing, it also supports free-hand editing, a challenging task for the layouter. We introduce how such a specification can be created and examine the advantages and shortcomings of each of either operating on the concrete syntax level or on the abstract syntax level