12739377
Word Complexity And Repetitions In Words
With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R(w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu…u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB, and Lempel-Ziv complexity, LZ. We have always R(w)≥LZ(w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word α being ultimately periodic is equivalent to: (i) , (ii) , and (iii) . De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R(w) can be computed in time and it is open, and probably very difficult, to find fast algorithms.
7865019
Follow automata
We give two new algorithms for constructing small nondeterministic finite automata (NFA) from regular expressions. The first constructs NFAs with e-transitions (eNFA) which are smaller than all the other eNFAs obtained by similar constructions. Their size is at most 3/2 |α| + 5/2, where α is the regular expression. This is very close to optimal since we prove also the lower bound 4/3; |α| + 5/2. The second constructs NFAs. It uses e-elimination in the eNFAs we just introduced and builds a quotient of the well-known position automaton w.r.t. the equivalence given by the follow relation; therefore giving the name of follow automaton. The new automaton uses optimally the information from the positions of a regular expression. We compare the follow automaton with the best constructions to date and show that it has important advantages over those.
27445105
Minimal cover-automata for finite languages
Abstract A cover-automaton A of a finite language L⊆Σ ∗ is a finite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L . A minimal deterministic finite cover automaton (DFCA) of a finite language L usually has a smaller size than a minimal DFA that accept L . Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In this paper, we describe an efficient algorithm that, for a given DFA accepting a finite language, constructs a minimal deterministic finite cover-automaton of the language. We also give algorithms for the boolean operations on deterministic cover automata, i.e., on the finite languages they represent.
546963
Decision Problems for Patterns
We settle an open problem, the inclusion problem for pattern languages. This is the first known case where inclusion is undecidable for generative devices having a trivially decidable equivalence problem. The study of patterns goes back to the seminal work of Thue and is important also, for instance, in recent work concerning inductive inference and learning. Our results concern both erasing and nonerasing patterns.
14075162
Synchronization Expressions: Characterization Results and Implementation
Synchronization expressions are defined as restricted regular expressions that specify synchronization constraints between parallel processes and their semantics is defined using the synchronization languages. In this paper we survey results on synchronization languages, in particular, various approaches to obtain a characterization of this language family using closure under a set of rewriting rules. Also, we discuss the use and implementation of synchronization expressions in a programming language designed for a parallel or distributed computing environment.
28358466
On Synchronization in P Systems
The P systems were recently introduced as distributed parallel computing models of a biochemical type. Multisets of objects are placed in a hierarchical structure of membranes and they evolve according to given rules, which are applied in a synchronous manner: at each step, all objects which can evolve, from all membranes, must evolve. We consider here the case when this restriction is removed. As expected, unsynchronized systems (even using catalysts) are weaker than the synchronized ones, providing that no priority relation among rules is considered. The power of P systems is not diminished when a priority is used and, moreover, the catalysts can change their states, among two possible states for each catalyst.
1394662
Dirichlet Enhanced Latent Semantic Analysis
This paper describes nonparametric Bayesian treatments for analyzing records containing occurrences of items. The introduced model retains the strength of previous approaches that explore the latent factors of each record (e.g. topics of documents), and further uncovers the clustering structure of records, which reflects the statistical dependencies of the latent factors. The nonparametric model induced by a Dirichlet process (DP) flexibly adapts model complexity to reveal the clustering structure of the data. To avoid the problems of dealing with infinite dimensions, we further replace the DP prior by a simpler alternative, namely Dirichlet-multinomial allocation (DMA), which maintains the main modelling properties of the DP. Instead of relying on Markov chain Monte Carlo (MCMC) for inference, this paper applies efficient variational inference based on DMA. The proposed approach yields encouraging empirical results on both a toy problem and text data. The results show that the proposed algorithm uncovers not only the latent factors, but also the clustering structure.
13332239
A Hierarchical Markov Random Field Model for Figure-Ground Segregation
To segregate overlapping objects into depth layers requires the integration of local occlusion cues distributed over the entire image into a global percept. We propose to model this process using hierarchical Markov random field (HMRF), and suggest a broader view that clique potentials in MRF models can be used to encode any local decision rules. A topology-dependent multiscale hierarchy is used to introduce long range interaction. The operations within each level are identical across the hierarchy. The clique parameters that encode the relative importance of these decision rules are estimated using an optimization technique called learning from rehearsals based on 2-object training samples. We find that this model generalizes successfully to 5-object test images, and that depth segregation can be completed within two traversals across the hierarchy. This computational framework therefore provides an interesting platform for us to investigate the interaction of local decision rules and global representations, as well as to reason about the rationales underlying some of recent psychological and neurophysiological findings related to figure-ground segregation.
946526
A Probabilistic Clustering-Projection Model for Discrete Data
For discrete co-occurrence data like documents and words, calculating optimal projections and clustering are two different but related tasks. The goal of projection is to find a low-dimensional latent space for words, and clustering aims at grouping documents based on their feature representations. In general projection and clustering are studied independently, but they both represent the intrinsic structure of data and should reinforce each other. In this paper we introduce a probabilistic clustering-projection (PCP) model for discrete data, where they are both represented in a unified framework. Clustering is seen to be performed in the projected space, and projection explicitly considers clustering structure. Iterating the two operations turns out to be exactly the variational EM algorithm under Bayesian model inference, and thus is guaranteed to improve the data likelihood. The model is evaluated on two text data sets, both showing very encouraging results.
11243052
Improving pseudo-relevance feedback in web information retrieval using web page segmentation
In contrast to traditional document retrieval, a web page as a whole is not a good information unit to search because it often contains multiple topics and a lot of irrelevant information from navigation, decoration, and interaction part of the page. In this paper, we propose a VIsion-based Page Segmentation (VIPS) algorithm to detect the semantic content structure in a web page. Compared with simple DOM based segmentation method, our page segmentation scheme utilizes useful visual cues to obtain a better partition of a page at the semantic level. By using our VIPS algorithm to assist the selection of query expansion terms in pseudo-relevance feedback in web information retrieval, we achieve 27% performance improvement on Web Track dataset.
2196967
Multiclass spectral clustering
We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigen-decomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We then solve an optimal discretization problem, which seeks a discrete solution closest to the continuous optima. The discretization is efficiently computed in an iterative fashion using singular value decomposition and nonmaximum suppression. The resulting discrete solutions are nearly global-optimal. Our method is robust to random initialization and converges faster than other clustering methods. Experiments on real image segmentation are reported.