Small NFAs from Regular Expressions: Some Experimental Results

Regular expressions (res), because of their succinctness and clear syntax, are the common choice to represent regular languages. However, efficient pattern matching or word recognition depend on the size of the equivalent nondeterministic finite automata (NFA). We present the implementation of several algorithms for constructing small epsilon-free NFAss from res within the FAdo system, and a comparison of regular expression measures and NFA sizes based on experimental results obtained from uniform random generated res. For this analysis, nonredundant res and reduced res in star normal form were considered.Comment: Proceedings of 6th Conference on Computability in Europe (CIE 2010), pages 194-203, Ponta Delgada, Azores, Portugal, June/July 201

Partial Derivative Automaton for Regular Expressions with Shuffle

We generalize the partial derivative automaton to regular expressions with shuffle and study its size in the worst and in the average case. The number of states of the partial derivative automata is in the worst case at most 2^m, where m is the number of letters in the expression, while asymptotically and on average it is no more than (4/3)^m

Use of a Digital Model Educational Training Model of Mental, Physical Education in Modern Technical in Progress

Presentamos en esta investigación un modelo pedagógico con utilización de las TIC para la enseñanza de la Física Moderna en el Instituto Federal. El modelo está adaptado a las teorías del aprendizaje significativo de Ausubel y modelos mentales, analizados e implementados para transformar el aprendizaje de la Física Moderna. Esta propuesta busca facilitar el aprendizaje a través de la construcción de mapas conceptuales para mostrar la formación de modelos mentales. Presentamos los resultados que muestran un resultado positivo referido al aprendizaje de los alumnos de tercer curso de una escuela secundaria.We report an experimental work at the Federal Institute in PortoAlegre, Brasil, where a professor in the physics laboratory and by using ICTs, establishes a teaching model for Modern Physics. Adapted theories, as Ausubel meaningful learning and mental models, are studied, analyzed and implemented in order to make the learning potentially effective. This proposed teaching model seeks to facilitate the learning process by means of concept maps which shows the mental models formation. Quantitative results show a positive impact in the learning of third graders of junior high school

Ideal regular languages and strongly connected synchronizing automata

We introduce the notion of a reset left regular decomposition of an ideal regular language, and we prove that the category formed by these decompositions with the adequate set of morphisms is equivalent to the category of strongly connected synchronizing automata. We show that every ideal regular language has at least one reset left regular decomposition. As a consequence, every ideal regular language is the set of synchronizing words of some strongly connected synchronizing automaton. Furthermore, this one-to-one correspondence allows us to introduce the notion of reset decomposition complexity of an ideal from which follows a reformulation of Černý's conjecture in purely language theoretic terms. Finally, we present and characterize a subclass of ideal regular languages for which a better upper bound for the reset decomposition complexity holds with respect to the general case

On Sum Graphs over Some Magmas

We consider the notions of sum graph and of relaxed sum graph over a magma, give several examples and results of these families of graphs over some natural magmas. We classify the cycles that are sum graphs for the magma of the subsets of a set with the operation of union, determine the abelian groups that provide a sum labelling of $C_4$, and show that $C_{4\ell}$ is a sum graph over the abelian group $\mathbb{Z}_f\times\mathbb{Z}_f$, where $f=f_{2\ell}$ is the corresponding Fibonacci number. For integral sum graphs, we give a linear upper bound for the radius of matchings, improving Harary's labelling for this family of graphs, and give the exact radius for the family of totally disconnected graphs. We found integer labellings for the 4D-cube, giving a negative answer to a question of Melnikov and Pyatikin, actually showing that the 4D-cube has infinitely many primitive labellings. We have also obtained some new results on mod sum graphs and relaxed sum graphs. Finally, we show that the direct product operation is closed for strong integral sum graphs

State Elimination Ordering Strategies: Some Experimental Results

Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blow-up in the worst-case. To overcome this, simple heuristic methods have been proposed. In this paper we analyse some of the heuristics presented in the literature and propose new ones. We also present some experimental comparative results based on uniform random generated deterministic finite automata.Comment: In Proceedings DCFS 2010, arXiv:1008.127