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.
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.
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.
10900126
Measures of Nondeterminism for Pushdown Automata
D. Vermeir and W. Savitch (Fund. Inform.4 (1981), 401-418) introduced two measures of nondeterminism for pushdown automata and showed interestingly that the second measure, which we refer to as the depth measure, yields an infinite hierarchy of language families between the deterministic context-free and general context-free languages. However, the proof given in op. cit. for this hierarchy theorem was incorrect. In this paper, using a pumping result for deterministic context-free languages we give a new proof for the strictness of the depth hierarchy. We introduce the monadic depth measure which is also shown to give rise to an infinite hierarchy of language families. Furthermore, we show that the monadic hierarchy is shifted by at most one level from the unrestricted depth hierarchy.
206058077
Synchronization Expressions with Extended Join Operation
Synchronization expressions are high level constructs used for specifying minimal synchronization constraints of parallel processes. Their semantics is defined by the corresponding synchronization language. The original definition of synchronization expressions [12, 13] forces the languages to be closed under rewriting rules that, for instance, do not preserve regularity. Here we propose an extension of the syntactic definition of synchronization expressions, and an appropriate modification of their semantics. The extended definition has the advantage that it allows us to eliminate the less well motivated transformations (rewriting rules) describing properties of synchronization languages. We show that the modified rewriting rules preserve regularity of the languages. Also, we obtain a characterization of finite synchronization languages as the family consisting of languages satisfying the start-termination property and closed under three types of simple rewriting rules.
329765
Unsupervised segmentation of color images
A novel technique for unsupervised learning in feature space is presented. The feature space is considered as composed of two distinct sources, "mode" and "valley", in the point of view of information theory. An entropy-based thresholding is taken to distinguish the discretized cells in the feature space. The cells labeled as "mode" are then chained to form mode areas. Thereafter a modified Akaike's information criterion is proposed to solve the cluster validity problem. After all the parameters are estimated, a labeling algorithm is developed based on the majority game theory. The method is applied to color image segmentation. The segmentation process is completely autonomous.
17974878
Variational Bayesian Dirichlet-Multinomial Allocation for Exponential Family Mixtures
This paper studies a Bayesian framework for density modeling with mixture of exponential family distributions. Variational Bayesian Dirichlet-Multinomial allocation (VBDMA) is introduced, which performs inference and learning efficiently using variational Bayesian methods and performs automatic model selection. The model is closely related to Dirichlet process mixture models and demonstrates similar automatic model selection in the variational Bayesian context.
9400780
Bayesian image classification using Markov random fields
In this paper, we present three optimisation techniques, Deterministic Pseudo-Annealing (DPA), Game Strategy Approach (GSA), and Modified Metropolis Dynamics (MMD), in order to carry out image classification using a Markov random field model. For the first approach (DPA), the a posteriori probability of a tentative labelling is generalised to a continuous labelling. The merit function thus defined has the same maxima under constraints yielding probability vectors. Changing these constraints convexifies the merit function. The algorithm solves this unambiguous maximisation problem, and then tracks down the solution while the original constraints are restored yielding a good, even if suboptimal, solution to the original labelling assignment problem. In the second method (GSA), the maximisation problem of the a posteriori probability of the labelling is solved by an optimisation algorithm based on game theory. A non-cooperative n-person game with pure strategies is designed such that the set of Nash equilibrium points of the game is identical to the set of local maxima of the a posteriori probability of the labelling. The algorithm converges to a Nash equilibrium. The third method (MMD) is a modified version of the Metropolis algorithm: at each iteration the new state is chosen randomly, but the decision to accept it is purely deterministic. This is also a suboptimal technique but it is much faster than stochastic relaxation. These three methods have been implemented on a Connection Machine CM2. Experimental results are compared to those obtained by the Metropolis algorithm, the Gibbs sampler and ICM (Iterated Conditional Mode).
14436503
Implementing a Model Checker for LEGO
Interactive theorem proving provides a general approach to modelling and verification of both hardware and software systems but requires significant human efforts to deal with many tedious proofs. To be effectively used in practice, we need some automatic tools such as model checkers to deal with those tedious proofs. In this paper, we formalise a verification system of both CCS and an imperative language in the proof development system LEGO which can be used to verify both finite and infinite problems. Then a model checker, LegoMC, is implemented to generate LEGO proof terms for finite-state problems automatically. Therefore people can use LEGO to verify a general problem with some of its finite sub-problems verified by LegoMC. On the other hand, this integration extends the power of model checking to verify more complicated and infinite models as well.
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.