10375023
A Pumping Lemma for Deterministic Context-Free Languages
Abstract In this paper, we introduce a new pumping lemma and a new iteration theorem for deterministic context-free languages (DCFLs). As application of the lemma, several languages are shown not to be deterministic context-free by using this lemma. An iteration theorem for DCFLs has already been introduced by Harrison in [3]. However, the result presented in this paper is different from his. Instead of considering the pumping property of individual words, we consider the pumping property of pairs of words. The latter approach seems more natural to the DCFLs (LR(1) languages). The pumping lemma introduced in this paper also appears to be easier to understand and use. We conjecture that there exist languages that can be shown not to be DCFLs by this new result but cannot be shown by the existing one. In Section 1, we introduce the basic notations used in this paper. In Section 2, we state our pumping lemma (without a proof) and show two applications of the lemma. In Section 3, a left-part theorem for LR ( k ) grammars is introduced, which is crucial to the proof of the pumping lemma and interesting on its own right. In the last section, we prove the lemma and extend it to an iteration theorem.
5352244
Minimal Cover-Automata for Finite Languages
A cover-automaton A of a finite language L ⊆ Σ * is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic cover automaton 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.
16103350
State Complexity of Regular Languages
State complexity is a descriptive complexity measure for regular languages. We investigate the problems related to the state complexity of regular languages and their operations. In particular, we compare the state complexity results on regular languages with those on nite languages.
26444044
Efficient Implementation of Regular Languages Using Reversed Alternating Finite Automata
Alternating finite automata (AFA) provide a natural and succinct way to denote regular languages. We introduce a bit-wise representation of reversed AFA (r-AFA) transition functions and describe an efficient implementation method for r-AFA and their operations using this representation. Experiments have shown that this implementation is much more efficient than, for instance, the Grail DFA implementation in both space and time.
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.
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.
11104953
Multi-Output Regularized Feature Projection
Dimensionality reduction by feature projection is widely used in pattern recognition, information retrieval, and statistics. When there are some outputs available (e.g., regression values or classification results), it is often beneficial to consider supervised projection, which is based not only on the inputs, but also on the target values. While this applies to a single-output setting, we are more interested in applications with multiple outputs, where several tasks need to be learned simultaneously. In this paper, we introduce a novel projection approach called multi-output regularized feature projection (MORP), which preserves the information of input features and, meanwhile, captures the correlations between inputs/outputs and (if applicable) between multiple outputs. This is done by introducing a latent variable model on the joint input-output space and minimizing the reconstruction errors for both inputs and outputs. It turns out that the mappings can be found by solving a generalized eigenvalue problem and are ready to extend to nonlinear mappings. Prediction accuracy can be greatly improved by using the new features since the structure of outputs is explored. We validate our approach in two applications. In the first setting, we predict users' preferences for a set of paintings. The second is concerned with image and text categorization where each image (or document) may belong to multiple categories. The proposed algorithm produces very encouraging results in both settings
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.
2791772
Segmentation induced by scale invariance
Perceptual organization is scale-invariant. In turn, a segmentation that separates features consistently at all scales is the desired one that reveals the underlying structural organization of an image. Addressing cross-scale correspondence with interior pixels, we develop this intuition into a general segmenter that handles texture and illusory contours through edges entirely without any explicit characterization of texture or curvilinearity. Experimental results demonstrate that our method not only performs on par with either texture segmentation or boundary completion methods on their specialized examples, but also works well on a variety of real images.
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.
38593151
Performance Comparison of a Deterministic and a Stochastic Method for Image Classification
In this paper, we compare the performances of two methods that we proposed for image classification. The first method is a stochastic approach which uses a Markov random field modelization. An optimization technique based on the game theory is used for the maximization of the a posteriori probability of the classes. The second method is a deterministic one which uses a feed-forward neural network. A novel learning method called projection learning is employed to train the neural network. The performances of these two methods are compared through their applications to image classification. The advantages and disadvantages of both methods, as well as possibilities to improve them are discussed.