Learning Residual Finite-State Automata Using Observation Tables

We define a two-step learner for RFSAs based on an observation table by using an algorithm for minimal DFAs to build a table for the reversal of the language in question and showing that we can derive the minimal RFSA from it after some simple modifications. We compare the algorithm to two other table-based ones of which one (by Bollig et al. 2009) infers a RFSA directly, and the other is another two-step learner proposed by the author. We focus on the criterion of query complexity.Comment: In Proceedings DCFS 2010, arXiv:1008.127

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

What Is a Macrostate? Subjective Observations and Objective Dynamics

We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of macrostates forms the unique maximal partition of phase space which 1) is consistent with our observations (a subjective fact about our ability to observe the system) and 2) obeys a Markov process (an objective fact about the system's dynamics). We review the ideas of computational mechanics, an information-theoretic method for finding optimal causal models of stochastic processes, and argue that macrostates coincide with the ``causal states'' of computational mechanics. Defining a set of macrostates thus consists of an inductive process where we start with a given set of observables, and then refine our partition of phase space until we reach a set of states which predict their own future, i.e. which are Markovian. Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables.Comment: 15 pages, no figure

Mathematical open problems in Projected Entangled Pair States

Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS.Comment: Notes associated to the Santal\'o Lecture 2017, Universidad Complutense de Madrid (UCM), minor typos correcte

Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales.Comment: 42 pages, 11 figures, 2 table

ON MONITORING LANGUAGE CHANGE WITH THE SUPPORT OF CORPUS PROCESSING

One of the fundamental characteristics of language is that it can change over time. One method to monitor the change is by observing its corpora: a structured language documentation. Recent development in technology, especially in the field of Natural Language Processing allows robust linguistic processing, which support the description of diverse historical changes of the corpora. The interference of human linguist is inevitable as it determines the gold standard, but computer assistance provides considerable support by incorporating computational approach in exploring the corpora, especially historical corpora. This paper proposes a model for corpus development, where corpus are annotated to support further computational operations such as lexicogrammatical pattern matching, automatic retrieval and extraction. The corpus processing operations are performed by local grammar based corpus processing software on a contemporary Indonesian corpus. This paper concludes that data collection and data processing in a corpus are equally crucial importance to monitor language change, and none can be set aside

Maximum a Posteriori Estimation by Search in Probabilistic Programs

We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variables. BaMC is an anytime MAP search algorithm applicable to any combination of random variables and dependencies. We compare BaMC to other MAP estimation algorithms and show that BaMC is faster and more robust on a range of probabilistic models.Comment: To appear in proceedings of SOCS1

An Algorithm for Pattern Discovery in Time Series

We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior exhibited in the data -- the underlying process's causal states. Unlike conventional methods for fitting hidden Markov models (HMMs) to data, our algorithm makes no assumptions about the process's causal architecture (the number of hidden states and their transition structure), but rather infers it from the data. It starts with assumptions of minimal structure and introduces complexity only when the data demand it. Moreover, the causal states it infers have important predictive optimality properties that conventional HMM states lack. We introduce the algorithm, review the theory behind it, prove its asymptotic reliability, use large deviation theory to estimate its rate of convergence, and compare it to other algorithms which also construct HMMs from data. We also illustrate its behavior on an example process, and report selected numerical results from an implementation.Comment: 26 pages, 5 figures; 5 tables; http://www.santafe.edu/projects/CompMech Added discussion of algorithm parameters; improved treatment of convergence and time complexity; added comparison to older method

Algorithms and implementation of functional dependency discovery in XML : a thesis presented in partial fulfilment of the requirements for the degree of Master of Information Sciences in Information Systems at Massey University

1.1 Background Following the advent of the web, there has been a great demand for data interchange between applications using internet infrastructure. XML (extensible Markup Language) provides a structured representation of data empowered by broad adoption and easy deployment. As a subset of SGML (Standard Generalized Markup Language), XML has been standardized by the World Wide Web Consortium (W3C) [Bray et al., 2004], XML is becoming the prevalent data exchange format on the World Wide Web and increasingly significant in storing semi-structured data. After its initial release in 1996, it has evolved and been applied extensively in all fields where the exchange of structured documents in electronic form is required. As with the growing popularity of XML, the issue of functional dependency in XML has recently received well deserved attention. The driving force for the study of dependencies in XML is it is as crucial to XML schema design, as to relational database(RDB) design [Abiteboul et al., 1995]