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Oblivious Two-Way Finite Automata: Decidability and Complexity

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LATIN 2012: Theoretical Informatics (LATIN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7256))

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Abstract

We investigate the descriptional complexity and decidability of obliviousness for two-way finite automata. In particular, we consider the simulation of two-way deterministic finite automata (\(\textrm{2DFA}\)s) by oblivious \(\textrm{2DFA}\)s, the simulation of oblivious \(\textrm{2DFA}\)s by sweeping \(\textrm{2DFA}\)s and one-way nondeterministic finite automata (\(\textrm{1NFA}\)s) as well as the simulation of sweeping \(\textrm{2DFA}\)s by \(\textrm{1NFA}\)s. In all cases exponential upper and lower bounds on the number of states are obtained for languages over an alphabet with at most four latters. Moreover, it is shown that obliviousness is decidable for \(\textrm{2DFA}\)s.

Supported by CRUI/DAAD under the project “Programma Vigoni: Descriptional Complexity of Non-Classical Computational Models.”

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References

  1. Berman, P., Lingas, A.: On the complexity of regular languages in terms of finite automata. Tech. Rep. 304, Polish Academy of Sciences (1977)

    Google Scholar 

  2. Birget, J.C.: Intersection and union of regular languages and state complexity. Inform. Process. Lett. 43, 185–190 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chrobak, M.: Finite automata and unary languages. Theoret. Comput. Sci. 47, 149–158 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Geffert, V.: Nondeterministic computations in sublogarithmic space and space constructibility. SIAM J. Comput. 20, 484–498 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Geffert, V., Mereghetti, C., Pighizzini, G.: Converting Two-Way Nondeterministic Unary Automata into Simpler Automata. Theoret. Comput. Sci. 295, 189–203 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Geffert, V., Pighizzini, G.: Two-way unary automata versus logarithmic space. Inform. Comput. 209, 1016–1025 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Glaister, I., Shallit, J.: A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59, 75–77 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gurari, E.M.: The equivalence problem for deterministic two-way sequential transducers is decidable. SIAM J. Comput. 11, 448–452 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Holzer, M.: Multi-head finite automata: data-independent versus data-dependent computations. Theoret. Comput. Sci. 286, 97–116 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Holzer, M., Kutrib, M.: Descriptional complexity – An introductory survey. In: Scientific Applications of Language Methods, pp. 1–58. Imperial College Press (2010)

    Google Scholar 

  11. Holzer, M., Kutrib, M., Malcher, A.: Multi-head finite automata: Origins and directions. Theoret. Comput. Sci. 412, 83–96 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  13. Hromkovič, J., Schnitger, G.: Nondeterminism versus Determinism for Two-way Finite Automata: Generalizations of Sipser’s Separation. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 439–451. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Hromkovič, J., Schnitger, G.: Lower bounds on the size of sweeping automata. Autom., Lang. Comb. 14, 23–31 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Kapoutsis, C.A.: Removing Bidirectionality from Nondeterministic Finite Automata. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 544–555. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Kapoutsis, C.A.: Two-Way Automata versus Logarithmic Space. In: Kulikov, A., Vereshchagin, N. (eds.) CSR 2011. LNCS, vol. 6651, pp. 359–372. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Lange, K.J., Niedermeier, R.: Data-Independences of Parallel Random Access Machines. In: Shyamasundar, R.K. (ed.) FSTTCS 1993. LNCS, vol. 761, pp. 104–113. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  18. Leung, H.: Tight lower bounds on the size of sweeping automata. Comput. System Sci. 63, 384–393 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Leung, H.: A technique for proving lower bounds on the size of sweeping automata. Autom., Lang. Comb. 14, 93–105 (2009)

    MathSciNet  MATH  Google Scholar 

  20. Lupanov, O.B.: A comparison of two types of finite sources. Problemy Kybernetiki 9, 321–326 (1963) (in Russian); German translation: Über den Vergleich zweier Typen endlicher Quellen. Probleme der Kybernetik 6, 328–335 (1966)

    Google Scholar 

  21. Mereghetti, C., Pighizzini, G.: Optimal simulations between unary automata. SIAM J. Comput. 30, 1976–1992 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: Symposium on Switching and Automata Theory (SWAT 1971), pp. 188–191. IEEE (1971)

    Google Scholar 

  23. Micali, S.: Two-way deterministic finite automata are exponentially more succinct than sweeping automata. Inform. Process. Lett. 12, 103–105 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  24. Moore, F.R.: On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata. IEEE Trans. Comput. 20, 1211–1214 (1971)

    Article  MATH  Google Scholar 

  25. Paterson, M.S., Fischer, M.J., Meyer, A.R.: An improved overlap argument for on-line multiplication. In: Complexity of Computation. SIAM-AMS Proceedings, vol. 7, pp. 97–112. AMS, New Jersey (1974)

    Google Scholar 

  26. Petersen, H.: The Head Hierarchy for Oblivious Finite Automata with Polynomial Advice Collapses. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 296–304. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  27. Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3, 114–125 (1959)

    Article  MathSciNet  Google Scholar 

  28. Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two way finite automata. In: Symposium on Theory of Computing (STOC 1978), pp. 275–286. ACM Press, New York (1978)

    Google Scholar 

  29. Sipser, M.: Lower bounds on the size of sweeping automata. Comput. System Sci. 21, 195–202 (1980)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib & Andreas Malcher

  2. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39, 20135, Milano, Italy

    Giovanni Pighizzini

Authors
  1. Martin Kutrib
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  2. Andreas Malcher
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  3. Giovanni Pighizzini
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Iowa State University, 50011, Ames, IA, USA

    David Fernández-Baca

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Kutrib, M., Malcher, A., Pighizzini, G. (2012). Oblivious Two-Way Finite Automata: Decidability and Complexity. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_44

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  • DOI: https://doi.org/10.1007/978-3-642-29344-3_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29343-6

  • Online ISBN: 978-3-642-29344-3

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