Efficient deterministic finite automata split-minimization derived from Brzozowski's algorithm

Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft s classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.García Gómez, P.; López Rodríguez, D.; Vázquez-De-Parga Andrade, M. (2014). Efficient deterministic finite automata split-minimization derived from Brzozowski's algorithm. International Journal of Foundations of Computer Science. 25(6):679-696. doi:10.1142/S0129054114500282S679696256Vázquez de Parga, M., García, P., & López, D. (2013). A polynomial double reversal minimization algorithm for deterministic finite automata. Theoretical Computer Science, 487, 17-22. doi:10.1016/j.tcs.2013.03.005Courcelle, B., Niwinski, D., & Podelski, A. (1991). A geometrical view of the determinization and minimization of finite-state automata. Mathematical Systems Theory, 24(1), 117-146. doi:10.1007/bf02090394POLÁK, L. (2005). MINIMALIZATIONS OF NFA USING THE UNIVERSAL AUTOMATON. International Journal of Foundations of Computer Science, 16(05), 999-1010. doi:10.1142/s0129054105003431Gries, D. (1973). Describing an algorithm by Hopcroft. Acta Informatica, 2(2). doi:10.1007/bf00264025Blum, N. (1996). An O(n log n) implementation of the standard method for minimizing n-state finite automata. Information Processing Letters, 57(2), 65-69. doi:10.1016/0020-0190(95)00199-9Knuutila, T. (2001). Re-describing an algorithm by Hopcroft. Theoretical Computer Science, 250(1-2), 333-363. doi:10.1016/s0304-3975(99)00150-

A sufficient condition to polynomially compute a minimum separating DFA

This is the author’s version of a work that was accepted for publication in Information Sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Sciences 370–371 (2016) 204–220. DOI 10.1016/j.ins.2016.07.053.The computation of a minimal separating automaton (MSA) for regular languages has been studied from many different points of view, from synthesis of automata or Grammatical Inference to the minimization of incompletely specified machines or Compositional Verification. In the general case, the problem is NP-complete, but this drawback does not prevent the problem from having a real application in the above-mentioned fields. In this paper, we propose a sufficient condition that guarantees that the computation of the MSA can be carried out with polynomial time complexity. © 2016 Elsevier Inc. All rights reserved.Vázquez-De-Parga Andrade, M.; García Gómez, P.; López Rodríguez, D. (2016). A sufficient condition to polynomially compute a minimum separating DFA. Information Sciences. 370-371:204-220. doi:10.1016/j.ins.2016.07.053S204220370-37

DFA minimization: Double reversal versus split minimization algorithms

“NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published inTheoretical Computer Science, [Volume 583, 7 June 2015, Pages 78–85] DOI 10.1016/j.tcs.2015.04.002In this paper, we show the relationship between the two most widely used approaches for the minimization of deterministic finite automata: minimization by split of partitions and minimization by double reversal. Even though the double reversal approach has usually been considered to be unconventional with respect to the more common split approach, we show that any double reversal minimization algorithm can be related to a split minimization algorithm and vice versa.García Gómez, P.; López Rodríguez, D.; Vázquez-De-Parga Andrade, M. (2015). DFA minimization: Double reversal versus split minimization algorithms. Theoretical Computer Science. 583:78-85. doi:10.1016/j.tcs.2015.04.002788558

Experiencia de clase inversa en el grado de ingeniería informática

La amplia disponibilidad de herramientas de generación de contenido multimedia hace posible la incorporación de nuevos recursos que complementen la actividad habitual en el aula. En la experiencia que se expone, se analizaron los recursos que existían relacionados con la materia de Teoría de Autómatas del Grado de Informática de la Universidad Politécnica de Valencia. Este análisis permitió detectar algunos aspectos clave que no eran convenientemente asimilados por el alumnado. Para cada uno de estos se elaboró material audiovisual que presentaba el contenido así como ejercicios de autoevaluación a realizar antes de la clase presencial. Se comprobó que el efecto de facilitar de forma anticipada al estudiante de este material permite al alumno, si bien en principio no completamente, trabajar ciertos conceptos, permitiendo plantear las dudas de forma más orientada. Pese a que el grupo piloto de esta experiencia estaba formado exclusivamente por voluntarios, lo que puede suponer un sesgo en la valoración, la experiencia se considera muy positiva

A split-based incremental deterministic automata minimization algorithm

The final publication is available at Springer via http://dx.doi.org/10.1007/s00224-014-9588-y. La fecha de publicación corresponde a la versión First OnlineWe here study previous results due to Hopcroft and Almeida et al. to propose an incremental split-based deterministic automata minimization algorithm whose average running-time does not depend on the size of the alphabet. The experimentation carried out shows that our proposal outperforms the algorithms studied whenever the automata have more than a (quite small) number of states and symbols.García Gómez, P.; Vázquez-De-Parga Andrade, M.; Velasco, JA.; López Rodríguez, D. (2014). A split-based incremental deterministic automata minimization algorithm. Theory of Computing Systems. 1-18. doi:10.1007/s00224-014-9588-y118Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley Publishing Company (1979)Watson, B.W., Daciuk, J.: An efficient incremental DFA minimization algorithm. Nat. Lang. Eng. 9(1), 49–64 (2003)Almeida, M., Moreira, N., Reis, R.: Incremental DFA minimisation. In: Domaratzki, M., Salomaa, K. (eds.) CIAA, of Lecture Notes in Computer Science, vol. 6482, pp 39–48. Springer (2010)Hopcroft, J.E.: An n ⋅ log n $n\cdot \log n$ algorithm for minimizing states in a finite automaton. Technical report, Stanford, University, Stanford (1971)Moore, E.F.: Gedanken experiments on sequential machines. In: Shannon, C.E., Mc-Carthy, J. (eds.) Automata Studies. Princeton Universty Press, Princeton (1956)Berstel, J., Boasson, L., Carton, O., Fagnot, I.: Automata: from Mathematics to Applications, chapter Minimization of automata. European Mathematical Society. (arXiv: 1010.5318v3. ) To appear.David, J.: Average complexity of Moore’s and Hopcroft’s algorithms. Theor. Comput. Sci. 417, 50–65 (2012)Almeida, M., Moreira, N., Reis, R.: Aspects of enumeration and generation with a string automata representation. In: Leung, H., Pighizzini, G. (eds.) DCFS, pp 58–69. New Mexico State University, Las Cruces (2006)Gries, D.: Describing an algorithm by Hopcroft. Acta Informatica 2, 97–109 (1973)Aho, A., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company (1974)Blum, N.: A O ( n log n ) $\mathcal {O}(n\log n)$ implementation of the standard method for minimizing n-state finite automata. Inf. Process. Lett. 57, 65–69 (1996)Knuutila, T.: Re-describing an algorithm by Hopcroft. Theor. Comput. Sci. 250, 333–363 (2001)Veanes, M.: Minimization of symbolic automata. Technical report, Microsoft Research, MSR-TR-2013-48 (2013)Lothaire, M.: Applied Combinatorics on Words chap. 1. Cambridge University Press, Cambridge (2005

DFA minimization: from Brzozowski to Hopcroft

Minimization of automata is a classic problem in Computer Sci- ence which is still studied nowadays. In this paper, we first propose a polynomial minimization method directly derived from Brzozowski¿s algorithm, and second, we show how the consideration of some effi- ciency improvements on this algorithm lead to obtain an algorithm equivalent to Hopcroft¿s.García Gómez, P.; López Rodríguez, D.; Vázquez-De-Parga Andrade, M. (2013). DFA minimization: from Brzozowski to Hopcroft. http://hdl.handle.net/10251/2762

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

Lattice-matched versus lattice-mismatched models to describe epitaxial monolayer graphene on Ru (0001)

Monolayer graphene grown on Ru(0001) surfaces forms a superstructure with periodic modulations in its geometry and electronic structure. The large dimension and inhomogeneous features of this superstructure make its description and subsequent analysis a challenge for theoretical modeling based on density functional theory. In this work, we compare two different approaches to describe the same physical properties of this surface, focusing on the geometry and the electronic states confined at the surface. In the more complex approach, the actual moiré structure is taken into account by means of large unit cells, whereas in the simplest one, the graphene moiré is completely neglected by representing the system as a stretched graphene layer that adapts pseudomorphically to Ru(0001). As shown in previous work, the more complex model provides an accurate description of the existing experimental observations. More interestingly, we show that the simplified stretched models, which are computationally inexpensive, reproduce qualitatively the main features of the surface electronic structure. They also provide a simple and comprehensive picture of the observed electronic structure, thus making them particularly useful for the analysis of these and maybe other complex interfacesWe thank Barcelona Supercomputing Center–Spanish Supercomputing Network (BSC-RES) and Centro de Computación Científica – Universidad Autónoma de Madrid (CCC-UAM) for allocation of computer time. Work supported by the MICINN Projects No. FIS2010-15127, No. FIS2010-18847, No. CTQ2010-17006, No. FIS-2010-19609- C09-00, No. ACI2008-0777, No. 2010C-07-25200, and No. CSD2007-00010, the CAM program NANOBIOMAGNET S2009/MAT1726 and the Gobierno Vasco-UPV/EHU Project No. IT-366-07. S.B. acknowledges financial support from MEC under FPU Grant No. AP-2007-00157. D.S. acknowledges financial support from the FPI-UAM grant progra

Resultados contrapuestos en una experiencia piloto de docencia inversa

El uso de la tecnología de la información y las comunicaciones permite explorar nuevas alternativas para la mejora del proceso de enseñanza-aprendizaje. En esta comunicación se exponen los resultados obtenidos en relación con la docencia de la materia de Teoría de Autómatas durante el segundo año de la experiencia piloto de implantación de la docencia inversa en el Grado de Informática de la Universidad Politécnica de Valencia. Los buenos resultados obtenidos por el equipo en el primer año sugirieron mantener el protocolo de trabajo y autoevaluación previa a la clase presencial. La experiencia limitada del primer año se mantuvo en un grupo exclusivo de matrícula voluntaria, extendiéndose además de forma puntual en la docencia de distintos grupos de matrícula ordinaria para valorar el efecto en grupos de mayor tamaño. Los resultados obtenidos en el segundo año no son comparables a los obtenidos el curso anterior, siendo necesaria una modificación del protocolo si se busca utilizar la docencia inversa en grupos de tamaño medio/alto

Electron localization in epitaxial graphene on Ru(0001) determined by moiré corrugation

The interpretation of scanning tunneling spectroscopy (STS) and scanning tunneling microscopy measurements of epitaxial graphene on lattice-mismatched substrates is a challenging problem, because of the spatial modulation in the electronic structure imposed by the formation of a moiré pattern. Here we describe the electronic structure of graphene adsorbed on Ru(0001) by means of density functional theory calculations that include van der Waals interactions and are performed on a large 11×11 unit cell to account for the observed moiré patterns. Our results show the existence of localized electronic states in the high and low areas of the moiré at energies close to and well above the Fermi level, respectively. Localization is due to the spatial modulation of the graphene-Ru(0001) interaction and is at the origin of the various peaks observed in STS spectraWork supported by the MICINN Projects No. FIS2010-15127, No. FIS2010-18847, No. CTQ2010-17006, No. FIS-2010-19609-C09-00, No. ACI2008-0777, No. 2010C-07-25200, and No. CSD2007-00010, the CAM program NANOBIOMAGNET S2009/MAT1726, and the Gobierno Vasco-UPV/EHU Project No. IT-366-07. S.B. acknowledges financial support from MEC under FPU Grant No. AP-2007-0015