Label Alphabet Research Articles

On the homology language of HDA models of transition systems

AbstractGiven a transition system with an independence relation on the alphabet of labels, one can associate with it a usually very large symmetric higher-dimensional automaton. The purpose of this paper is to show that by choosing an acyclic relation whose symmetric closure is the given independence relation, it is possible to construct a much smaller nonsymmetric HDA with the same homology language.

Representation of deterministic graphs by defining pair of words

The paper proposes a representation of deterministic graphs (D-graphs) by sets of words in the alphabet of labels of their vertices. Nowadays graphs are a conceptual tool for analytics, development and testing of various software. Among all graphs, there is a subclass of labeled graphs whose elements have labels from a predefined alphabet. Such graphs are actively used to describe and model computational processes in programming, robotics, model verification and validation, etc. Labeled graphs are an information environment for mobile agents, whose movement along the graph can be represented by sequences of vertex labels - words in the label alphabet. A vertex-labeled graph is said to be D-graph if all vertices in the neighborhood of every its vertex have different labels. For such graphs, in the case when its graph map (i.e., the set of vertices and edges and the labeling function) and the initial vertex from which the agents start their movements are known, there is an unambiguous correspondence between the sequence of labels of the vertices visited by the agent and the trajectory of this agent's movements in the graph. In the case when the map of the studied D-graph is unknown to an external observer, the movements of agents can be organized in such a way that, based on their analysis, the observer receives the desired information about the structure of the graph (for example, the map of the graph, the shortest paths between vertices, comparison of the studied graph with the reference graph). Such an analysis can significantly simplify the linguistic representation of a D-graph - the mapping of a graph to one or more finite sets of words in the alphabet of graph vertex labels, which can be used to reconstruct the graph. In this paper, we propose a representation of deterministic graphs by a defining pair of word sets, the first component of which describes the cycles of the graph, and the second - its leaf vertices. This representation is analogous to the system of defining relations for automata. We proposed the algorithm, that for any pair of sets, builds a D-graph for which this pair is deterministic, or reports that it is impossible to do so is given. The algorithm for constructing a canonical defining pair for a D-graph is also given and numerical estimates of this pair for D-graphs with a known number of vertices and edges are found. Further directions of research on this topic are outlined. The results will allow to use new methods and algorithms for solving problems of analysis of graphs with marked vertices.

Metric properties of the canonical defining pair for determined graphs

The aim of this paper is to study the representation of deterministic graphs (D-graphs) by sets of words over the vertex labels alphabet and to find metric properties of this representation. Vertex-labeled graphs are widely used in various computational processes modeling in programming, robotics, model checking, etc. In such models graphs playing the role of an information environment of single or several mobile agents. Walks of agents on a graph determines the sequence of vertices labels or words in the alphabet of labels. A vertex-labeled graph is said to be D-graph if all vertices in the neighborhood of every its vertex have different labels. For D-graphs in case when the graph as a whole and the initial vertex (i.e. the vertex from which the agent started walking) are known there exists the one-to-one correspondence between the sequence of vertices visited by the agent and the trajectory of its walks on the graph. In case when the D-graph is not known as a whole, agent walks on it can be arranged in such way that an observer obtains information about the structure of the graph sufficient to solve the problems of graph recognizing, finding optimal path between vertices, comparison between current graph and etalon graph etc. This paper specifies the representation of D-graphs by the defining pair of sets of words (the first describes cycles of the graph and the second -- all its vertices of degree 1). This representation is an analogue of the system of defining relations for everywhere defined automata. The structure of the so-called canonical defining pair, which is minimal in terms of the number of words, is also considered. An algorithm for building such pair is developed and described in detail. For D-graphs with a given number of vertices and edges, the exact number of words in the first component of its canonical defining pair and the minimum and maximum attainable bounds for the the number of words in the second component of this pair are obtained. This representation allows us to use new methods and algorithms to solve the problems of analyzing vertex-labeled graphs.

Labelled graph rules in P systems

P systems with graph productions were introduced by Freund in 2004. It was shown that such a variant of P system can generate any recursively enumerable language of weakly connected graphs. In this paper, we consider such P systems where the input is any connected graph and each graph production is labelled over an alphabet. We name the system as Process Guided P System where the computation is guided by a string over the set of labels. The set of all strings over the label alphabet which results in the halting computation of the system forms a guiding language of the system. We compare such guiding languages with Chomsky hierarchy. Two direct applications of this variant are also given.

Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions

A language L over a finite alphabet Σ is growth sensitive (or entropy sensitive) if forbidding any finite set of factors F of L yields a sublanguage LF whose exponential growth rate (entropy) is smaller than that of L. Let (X,E,ℓ) be an infinite, oriented, edge-labelled graph with label alphabet Σ. Considering the graph as an (infinite) automaton, we associate with any pair of vertices x,y∈X the language Lx,y consisting of all words that can be read as labels along some path from x to y. Under suitable general assumptions, we prove that these languages are growth sensitive. This is based on using Markov chains with forbidden transitions.

Realizability of words in mosaic labyrinths

In this paper we study mosaic labyrinths with the help of words generated by them in the alphabet of labels attached to arcs and vertices of a labyrinth. We consider the problem of the characterization of words generated by a labyrinth. We propose a constructive recognition criterion, it defines whether a word is generated by a labyrinth or not. We establish conditions under which a word can be generated by a unique labyrinth, by a finite number of labyrinths, or by infinitely many labyrinths.

Predicting and Learning RNA Secondary Structures

It is of great signi cance to develop an e cient software system for higher-level structural prediction in RNA/protein sequences. Speaking of RNA secondary structure prediction, it is inevitably required that a prediction system must have an ability to deal with so-called pseudoknot structures, one of the most typical and important constructs found in vivo, while no e ective system is yet reported for predicting RNA secondary structures involving in pseudoknots. We are developing prediction systems for RNA secondary structures that can handle pseudo-knots in an elegant manner, where the developing systems are constructed based on the following two ways. Prediction System Using Tree Grammars : In the previous work[3], we developed a parsing algorithm for RNA modeling grammars, and applied it to some computational problems concerning RNA secondary structures. In this work, we prototype a prediction system for RNA secondary structures which is based on minimizing the free-energy change associated with base pairings and loop structures. One of the major advantages of this system is its capability of predicting structures which include pseudoknots. We evaluate the system by presenting how long sequences it can process and how long and how much memory it takes to nd the solution. We also make comparisons between biologically observed structures and prediction results. Learning Secondary Structures Using Control Sets : We propose a learning system that acquires the common RNA secondary structures of the given set of RNA sequences. In order to capture the common biological features of RNA secondary structures, it is possible to make use of derivational information obtained from parsing analysis by the prediction system described above. More speci cally, the key idea of our method is outlined as follows: Initially we set up the most general tree grammar G0 = (C; A; fSg), where every nonterminal node in each tree of C or A is labeled by exactly one symbol S, and A contains all types of uniquely labeled adjunct trees. Thus G0 has no restriction on which adjunct trees to use at any con guration within the derivation. Then, given RNA sequences are parsed by the prediction system (parser), to get the control words (i.e., words over the alphabet of labels of all trees). Our learning system for RNA secondary structures consists of the following procedures: 1. Set up the most general tree grammar G0, 2. Parse the given sequence with G0 using the parser mentioned above, 3. Construct a set of control words, 4. Learn the control set. In this manner, given a set of RNA sequences, the learning system produces a control set with which one can construct a prediction system together with G0. In other words, one may have another type of prediction system using control set.

Automatic determination of labels and Markov word models in a speech recognition system

In a Markov model speech recognition system, an acoustic processor generates one label after another selected from an alphabet of labels. Each vocabulary word is represented as a baseform constructed of a sequence of Markov models. Each Markov model is stored in a computer memory as (a) a plurality of states; (b) a plurality of arcs, each extending from a state to a state with a respective stored probability; and (c) stored label output probabilities, each indicating the likelihood of a given label being produced at a certain arc. Word likelihood based on acoustic characteristics is determined by matching a string of labels generated by the acoustic processor against the probabilities stored for each word baseform. The present invention involves the specifying of label parameters and the constructing of word baseforms interdependently in a Markov model speech recognition system to improve system performance.

On the editing distance between unordered labeled trees

This paper considers the problem of computing the editing distance between unordered, labeled trees. We give efficient polynomial-time algorithms for the case when one tree is a string or has a bounded number of leaves. By contrast, we show that the problem is NP-complete even for binary trees having a label alphabet of size two.

Speech recognition method

For circumstance adaption, for example, speaker adaption, confusion coefficients between the labels of the label alphabet for initial training and those for adaption are determined by alignment of adaption speech with the corresponding initially trained Markov model. That is, each piece of adaptation speech is aligned with a corresponding initially trained Markov model by the Viterbi algorithm, and each label in the adaption speech is mapped onto one of the states of the Markov models. In respect of each adaptation lable ID, the parameter values for each initial training label of the states which are mapped onto the adaptation label in concern are accumulated and normalized to generate a confusion coefficient between each initial training label and each adaptation label. The parameter table of each Markov model is rewritten in respect of the adaptation label alphabet using the confusion coefficients.