Learning Rational Functions

International audienceRational functions are transformations from words to words that can be defined by string transducers. Rational functions are also captured by deterministic string transducers with lookahead. We show for the first time that the class of rational functions can be learned in the limit with polynomial time and data, when represented by string transducers with lookahead in the diagonal-minimal normal form that we introduce

Fundamento del derecho natural según los principios de la doctrina de la ciencia

1.-El carácter de la racionalidad consiste en que el agente [das Handelnde] y lo actuado [das Behandelte] son uno y lo mismo; y con esta descripción se ha agotado el ámbito de la razón como tal. El uso del lenguaje ha depositado en la palabra Yo este concepto sublime para aquéllos que son capaces de él, para los que son capaces de la abstracción de su propio Yo

Synthesizing Program Input Grammars

We present an algorithm for synthesizing a context-free grammar encoding the language of valid program inputs from a set of input examples and blackbox access to the program. Our algorithm addresses shortcomings of existing grammar inference algorithms, which both severely overgeneralize and are prohibitively slow. Our implementation, GLADE, leverages the grammar synthesized by our algorithm to fuzz test programs with structured inputs. We show that GLADE substantially increases the incremental coverage on valid inputs compared to two baseline fuzzers

Minimal Synthesis of String To String Functions From Examples

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.Comment: SYNT 201

Inducing Probabilistic Grammars by Bayesian Model Merging

We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are {\em incorporated} by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are {\em merged} to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models (`Occam's Razor'). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based $n$-grams, and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13 page

Olive oil consumption and all-cause, cardiovascular and cancer mortality in an adult mediterranean population in Spain

Objective: We assessed the association between usual olive oil consumption (OOC) and all-cause, cardiovascular (CVD) and cancer mortality in an adult population in Spain. Materials and methods: OOC was evaluated at baseline in 1,567 participants aged 20 years and older from the Valencia Nutrition Study in Spain using validated food frequency questionnaires. During an 18-year follow-up period, 317 died, 115 due to CVD and 82 due to cancer. Cox regression models were used to estimate adjusted hazard ratios (HR) and 95% confidence intervals (95%CI). Results: After adjusting for demographic and lifestyle factors, the OOC was associated with a lower risk of all-cause, CVD and cancer mortality. Compared to the less than once per month consumption, the consumption of up to one tablespoon per day was associated with a 9% lower risk of all-cause mortality (HR: 0.91; 95%CI: 0.68-1.22) and the consumption of 2 or more tablespoons with a 31% lower risk of all-cause mortality (HR: 0.69; 95%CI: 0.50–0.93; p-trend = 0.011). The consumption of 2 or more tablespoons per day was also associated with lower risk of mortality for CVD (HR: 0.54; 95%CI: 0.32–0.91; p-trend = 0.018) and cancer (HR: 0.49, 95%CI: 0.26–0.94; p-trend = 0.019). Conclusion: Higher olive oil consumption was associated with lower long-term risk of all-cause, CVD and cancer mortality in an adult Mediterranean population. The maximum benefit was observed for the consumption of two or more tablespoons per day. Copyright © 2022 Torres-Collado, García-de la Hera, Lopes, Compañ-Gabucio, Oncina-Cánovas, Notario-Barandiaran, González-Palacios and Vioque.The VNS study was supported by a grant from the Dirección General de Salud Pública, Generalitat Valenciana 1994 and the Fondo Investigacion Sanitaria (FIS 00/0985). This study has also received support from the Instituto de Salud Carlos III FEDER funds (FIS PI13/00654), CIBER of Epidemiology and Public Health (CIBERESP), CB06/02/0013 and ISABIAL

Melody recognition with learned edit distances

In a music recognition task, the classification of a new melody is often achieved by looking for the closest piece in a set of already known prototypes. The definition of a relevant similarity measure becomes then a crucial point. So far, the edit distance approach with a-priori fixed operation costs has been one of the most used to accomplish the task. In this paper, the application of a probabilistic learning model to both string and tree edit distances is proposed and is compared to a genetic algorithm cost fitting approach. The results show that both learning models outperform fixed-costs systems, and that the probabilistic approach is able to describe consistently the underlying melodic similarity model.This work was funded by the French ANR Marmota project, the Spanish PROSEMUS project (TIN2006-14932-C02), the research programme Consolider Ingenio 2010 (MIPRCV, CSD2007-00018), and the Pascal Network of Excellence

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

Equivalence of Deterministic Nested Word to Word Transducers

International audienceWe study the equivalence problem of deterministic nested word to word transducers and show it to be surprisingly robust. Modulo polynomial time reductions, it can be identified with 4 equivalence problems for diverse classes of deterministic non-copying order-preserving transducers. In particular, we present polynomial time back and fourth reductions to the morphism equivalence problem on context free languages, which is known to be solvable in polynomial time

Learning deterministic probabilistic automata from a model checking perspective

Probabilistic automata models play an important role in the formal design and analysis of hard- and software systems. In this area of applications, one is often interested in formal model-checking procedures for verifying critical system properties. Since adequate system models are often difficult to design manually, we are interested in learning models from observed system behaviors. To this end we adopt techniques for learning finite probabilistic automata, notably the Alergia algorithm. In this paper we show how to extend the basic algorithm to also learn automata models for both reactive and timed systems. A key question of our investigation is to what extent one can expect a learned model to be a good approximation for the kind of probabilistic properties one wants to verify by model checking. We establish theoretical convergence properties for the learning algorithm as well as for probability estimates of system properties expressed in linear time temporal logic and linear continuous stochastic logic. We empirically compare the learning algorithm with statistical model checking and demonstrate the feasibility of the approach for practical system verification