Grammars with two-sided contexts

In a recent paper (M. Barash, A. Okhotin, "Defining contexts in context-free grammars", LATA 2012), the authors introduced an extension of the context-free grammars equipped with an operator for referring to the left context of the substring being defined. This paper proposes a more general model, in which context specifications may be two-sided, that is, both the left and the right contexts can be specified by the corresponding operators. The paper gives the definitions and establishes the basic theory of such grammars, leading to a normal form and a parsing algorithm working in time O(n^4), where n is the length of the input string.Comment: In Proceedings AFL 2014, arXiv:1405.527

Structure induction by lossless graph compression

This work is motivated by the necessity to automate the discovery of structure in vast and evergrowing collection of relational data commonly represented as graphs, for example genomic networks. A novel algorithm, dubbed Graphitour, for structure induction by lossless graph compression is presented and illustrated by a clear and broadly known case of nested structure in a DNA molecule. This work extends to graphs some well established approaches to grammatical inference previously applied only to strings. The bottom-up graph compression problem is related to the maximum cardinality (non-bipartite) maximum cardinality matching problem. The algorithm accepts a variety of graph types including directed graphs and graphs with labeled nodes and arcs. The resulting structure could be used for representation and classification of graphs.Comment: 10 pages, 7 figures, 2 tables published in Proceedings of the Data Compression Conference, 200

Stepping from Graph Transformation Units to Model Transformation Units

Graph transformation units are rule-based entities that allow to transform source graphs into target graphs via sets of graph transformation rules according to a control condition. The graphs and rules are taken from an underlying graph transformation approach. Graph transformation units specify model transformations whenever the transformed graphs represent models. This paper is based on the observation that in general models are not always suitably represented as single graphs, but they may be specified as the composition of a variety of different formal structures such as sets, tuples, graphs, etc., which should be transformed by compositions of different types of rules and operations instead of single graph transformation rules. Consequently, in this paper, graph transformation units are generalized to model transformation units that allow to transform such kind of composed models in a rule-based and controlled way. Moreover, two compositions of model transformation units are presented

Towards the uniform manipulation of visual and textual languages in AToM3

This is an electronic version of the paper presented at the III Jornadas de Programación y Lenguajes, held in Alicante on 2003This paper presents the approach taken in the multi-paradigm tool AToM3 for the integration of textual and visual languages in a uniform framework. The tool is used for the modelling, analysis and simulation of complex (physical or software) systems, where each system component may have to be described using a different formalism. The different visual or textual formalisms can be described in the form of meta-models using graphical, high-level notations such as Entity Relationship or UML class diagrams. From these descriptions, AToM3 is able to generate a customized modelling tool for the specified formalism. Models at any meta-level are stored as attributed, typed graphs and thus can be manipulated (simulated, transformed, optimized, etc.) by attributed graph grammars. In the case of a textual notation, from the meta-model description a front-end parser is semi-automatically generated that transforms the textual models into abstract syntax graphs (instances of the meta-model), and thus can be manipulated in a uniform way with the other visual notations. To illustrate these concepts, we present an example in which we define a meta-model for Computational Tree Logic and generate visual and textual parsers for the formalism.We would like to aknowledge the Spanish Ministry of Science and Technology (project TIC2002-01948) for partially supporting this work

Graph Tuple Transformation

Graph transformation units are rule-based devices to model and compute relations between initial and terminal graphs. In this paper, they are generalized to graph tuple transformation units that allow one to combine different kinds of graphs into tuples and to process the component graphs simultaneously and interrelated with each other. Moreover, one may choose some of the working components as inputs and some as outputs such that a graph tuple transformation unit computes a relation between input and output tuples of potentially different kinds of graphs rather than a binary relation on a single kind of graphs

Polynomial Time Algorithms for Multi-Type Branching Processes and Stochastic Context-Free Grammars

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where \epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open problems regarding the computational complexity of computing key quantities associated with some classic and heavily studied stochastic processes, including multi-type branching processes and stochastic context-free grammars

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