Polynomial characteristic sets for DFA identification

[EN] We study the order in Grammatical Inference algorithms, and its influence on the polynomial (with respect to the data) identification of languages. This work is motivated by recent results on the polynomial convergence of data-driven grammatical inference algorithms. In this paper, we prove a sufficient condition that assures the existence of a characteristic sample whose size is polynomial with respect to the minimum DFA of the target language. © 2012 Elsevier B.V. All rights reserved.Work partially supported by the Spanish Ministerio de Economia y Competitividad under research project TIN2011-28260-C03-01 and Universidad Politecnica de Valencia grant PAID-2019-06-2011.García Gómez, P.; López Rodríguez, D.; Vázquez-De-Parga Andrade, M. (2012). Polynomial characteristic sets for DFA identification. Theoretical Computer Science. 448:41-46. https://doi.org/10.1016/j.tcs.2012.04.042S414644

Learning Moore Machines from Input-Output Traces

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample

Finite automata and algebraic extensions of function fields

We give an automata-theoretic description of the algebraic closure of the rational function field F_q(t) over a finite field, generalizing a result of Christol. The description takes place within the Hahn-Mal'cev-Neumann field of "generalized power series" over F_q. Our approach includes a characterization of well-ordered sets of rational numbers whose base p expansions are generated by a finite automaton, as well as some techniques for computing in the algebraic closure; these include an adaptation to positive characteristic of Newton's algorithm for finding local expansions of plane curves. We also conjecture a generalization of our results to several variables.Comment: 40 pages; expanded version of math.AC/0110089; v2: refereed version, includes minor edit

Learning probability distributions generated by finite-state machines

We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft

Long-range correlation and multifractality in Bach's Inventions pitches

We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view we find same second moment exponents (after double profiling) in ranges (1.7-1.8) in his works. Comparing MF-DFA results of original series to those for shuffled and surrogate series we can distinguish multifractality due to long-range correlations and a broad probability density function. Finally we determine the scaling exponents and singularity spectrum. We conclude fat tail has more effect in its multifractality nature than long-range correlations.Comment: 18 page, 6 figures, to appear in JSTA

Inferring Symbolic Automata

We study the learnability of symbolic finite state automata, a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all obtained results are positive. We provide a necessary condition for efficient learnability of SFAs in this paradigm, from which we obtain the first negative result. The main focus of our work lies in the learnability of SFAs under the paradigm of identification in the limit using polynomial time and data. We provide a necessary condition and a sufficient condition for efficient learnability of SFAs in this paradigm, from which we derive a positive and a negative result