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Adding Pebbles to Weighted Automata

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Implementation and Application of Automata (CIAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7381))

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Abstract

We extend weighted automata and weighted rational expressions with 2-way moves and (reusable) pebbles. We show with examples from natural language modeling and quantitative model-checking that weighted expressions and automata with pebbles are more expressive and allow much more natural and intuitive specifications than classical ones. We extend Kleene-Schützenberger theorem showing that weighted expressions and automata with pebbles have the same expressive power. We focus on an efficient translation from expressions to automata. We also prove that the evaluation problem for weighted automata can be done very efficiently if the number of (reusable) pebbles is low.

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References

  1. Allauzen, C., Mohri, M.: A Unified Construction of the Glushkov, Follow, and Antimirov Automata. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 110–121. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Berry, G., Sethi, R.: From regular expressions to deterministic automata. Theoretical Computer Science 48, 117–126 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Berstel, J., Reutenauer, C.: Noncommutative rational series with applications, Cambridge. Encyclopedia of Mathematics & Its Applications, vol. 137 (2011)

    Google Scholar 

  4. Birget, J.-C.: State-complexity of finite-state devices, state compressibility and incompressibility. Theory of Computing Systems 26, 237–269 (1993)

    MathSciNet  MATH  Google Scholar 

  5. Bojańczyk, M.: Tree-Walking Automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 1–2. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Bojańczyk, M., Samuelides, M., Schwentick, T., Segoufin, L.: Expressive Power of Pebble Automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 157–168. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Bollig, B., Gastin, P.: Weighted versus Probabilistic Logics. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 18–38. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Bollig, B., Gastin, P., Monmege, B., Zeitoun, M.: Pebble Weighted Automata and Transitive Closure Logics. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 587–598. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Brüggeman-Klein, A.: Regular expressions into finite automata. Theoretical Computer Science 120, 197–213 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Brüggeman-Klein, A., Wood, D.: Caterpillars: A context specification technique. Markup Languages 2(1), 81–106 (2000)

    Article  Google Scholar 

  11. Brzozowski, J.A., McCluskey, E.J.: Signal flow graph techniques for sequential circuit state diagrams. IEEE Trans. on Electronic Computers 12(9), 67–76 (1963)

    Article  MATH  Google Scholar 

  12. Buchholz, P., Kemper, P.: Model checking for a class of weighted automata. Discrete Event Dynamic Systems 20(1), 103–137 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ciesinski, F., Größer, M.: On Probabilistic Computation Tree Logic. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 147–188. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Conway, J.: Regular Algebra and Finite Machines. Chapman & Hall (1971)

    Google Scholar 

  15. Droste, M., Kuich, W.: Semirings and formal power series. In: Handbook of Weighted Automata [16], ch. 1, pp. 3–27

    Google Scholar 

  16. Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. EATCS Monographs in Theoretical Computer Science. Springer (2009)

    Google Scholar 

  17. Engelfriet, J., Hoogeboom, H.J.: Tree-walking pebble automata. In: Jewels are Forever, pp. 72–83. Springer (1999)

    Google Scholar 

  18. Ésik, Z., Kuich, W.: Modern Automata Theory. Electronic book (2007), http://dmg.tuwien.ac.at/kuich

  19. Globerman, N., Harel, D.: Complexity results for two-way and multi-pebble automata and their logics. Theoretical Computer Science 169, 161–184 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Glushkov, V.M.: The abstract theory of automata. Russian Math. Surveys 16, 1–53 (1961)

    Article  Google Scholar 

  21. Knight, K., May, J.: Applications of weighted automata in natural language processing. In: Handbook of Weighted Automata [16], ch. 14, pp. 555–579

    Google Scholar 

  22. Kuske, D.: Schützenberger’s theorem on formal power series follows from kleene’s theorem. Theoretical Computer Science 401(1-3), 243–248 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mandrali, E.: Weighted LTL with Discounting. In: Moreira, N., Reis, R. (eds.) CIAA 2012. LNCS, vol. 7381, pp. 353–360. Springer, Heidelberg (2012)

    Google Scholar 

  24. McNaughton, R., Yamada, H.: Regular expressions and state graphs for automata. IRE Trans. on Electronic Computers 9(1), 39–47 (1960)

    Article  Google Scholar 

  25. Meinecke, I.: A Weighted μ-Calculus on Words. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 384–395. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  26. Ravikumar, B.: On some variations of two-way probabilistic finite automata models. Theoretical Computer Science 376(1-2), 127–136 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press (2009)

    Google Scholar 

  28. Sakarovitch, J.: Rational and recognisable power series. In: Handbook of Weighted Automata [16], ch. 4, pp. 103–172

    Google Scholar 

  29. Sakarovitch, J.: Automata and expressions. In: AutoMathA Handbook (to appear, 2012)

    Google Scholar 

  30. Samuelides, M., Segoufin, L.: Complexity of Pebble Tree-Walking Automata. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 458–469. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  31. Schützenberger, M.-P.: On the definition of a family of automata. Information and Control 4, 245–270 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  32. Vardi, M.: The complexity of relational query languages. In: Proceedings of STOC 1982, pp. 137–146. ACM Press (1982)

    Google Scholar 

  33. Vardi, M.: On the complexity of bounded-variable queries. In: Proceedings of PODS 1995, pp. 266–276. ACM Press (1995)

    Google Scholar 

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Authors and Affiliations

  1. CNRS, Inria, LSV, ENS Cachan, France

    Paul Gastin & Benjamin Monmege

Authors
  1. Paul Gastin
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  2. Benjamin Monmege
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Editors and Affiliations

  1. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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Gastin, P., Monmege, B. (2012). Adding Pebbles to Weighted Automata. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-31606-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31605-0

  • Online ISBN: 978-3-642-31606-7

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