On periodic points of free inverse monoid endomorphisms

It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky's hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid can be represented by a context-sensitive language but, in general, it cannot be represented by a context-free language.Comment: 18 page

Grammar induction for mildly context sensitive languages using variational Bayesian inference

The following technical report presents a formal approach to probabilistic minimalist grammar induction. We describe a formalization of a minimalist grammar. Based on this grammar, we define a generative model for minimalist derivations. We then present a generalized algorithm for the application of variational Bayesian inference to lexicalized mildly context sensitive language grammars which in this paper is applied to the previously defined minimalist grammar

Learning bidimensional context dependent models using a context sensitive language

International Conference on Pattern Recognition (ICPR), 1996, Viena (Austria)Automatic generation of models from a set of positive and negative samples and a-priori knowledge (if available) is a crucial issue for pattern recognition applications. Grammatical inference can play an important role in this issue since it can be used to generate the set of model classes, where each class consists on the rules to generate the models. In this paper we present the process of learning context dependent bidimensional objects from outdoors images as context sensitive languages. We show how the process is conceived to overcome the problem of generalizing rules based on a set of samples which have small differences due to noisy pixels. The learned models can be used to identify objects in outdoors images irrespectively of their size and partial occlusions. Some results of the inference procedure are shown in the paper.Peer Reviewe

Further Results on the Power of Generating APCol Systems

In this paper we continue our investigations in APCol systems (Automatonlike P colonies), variants of P colonies where the environment of the agents is given by a string and the functioning of the system resembles to the functioning of standard nite automaton. We rst deal with the concept of determinism in these systems and compare deterministic APCol systems with deterministic register machines. Then we focus on generating non-deterministic APCol systems with only one agent. We show that these systems are as powerful as 0-type grammars, i.e., generate any recursively enumerable language. If the APCol system is non-erasing, then any context-sensitive language can be generated by a non-deterministic APCol systems with only one agent

Evolino for recurrent support vector machines

Traditional Support Vector Machines (SVMs) need pre-wired finite time windows to predict and classify time series. They do not have an internal state necessary to deal with sequences involving arbitrary long-term dependencies. Here we introduce a new class of recurrent, truly sequential SVM-like devices with internal adaptive states, trained by a novel method called EVOlution of systems with KErnel-based outputs (Evoke), an instance of the recent Evolino class of methods. Evoke evolves recurrent neural networks to detect and represent temporal dependencies while using quadratic programming/support vector regression to produce precise outputs. Evoke is the first SVM-based mechanism learning to classify a context-sensitive language. It also outperforms recent state-of-the-art gradient-based recurrent neural networks (RNNs) on various time series prediction tasks.Comment: 10 pages, 2 figure

Contextual Injustice

Contextualist treatments of clashes of intuitions can allow that two claims, apparently in conflict, can both be true. But making true utterances is far from the only thing that matters — there are often substantive normative questions about what contextual parameters are appropriate to a given conversational situation. This paper foregrounds the importance of the social power to set contextual standards, and how it relates to injustice and oppression, introducing a phenomenon I call "contextual injustice," which has to do with the unjust manipulation of conversational parameters in context-sensitive discourse. My central example applies contextualism about knowledge ascriptions to questions about knowledge regarding sexual assault allegations, but I will also discuss parallel dynamics in other examples of context-sensitive language involving politically significant terms, including gender terms. The central upshot is that the connections between language, epistemology, and social justice are very deeply interlinked