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Computer Science

Weighted Automata–Theory and Applications

Profile image of Manfred DrosteManfred Droste

Abstract

We extend the disambiguation construction presented by Mohri and Riley [1] in two ways. First we change the underlying structure of their automata from words to trees and second we show that these results hold not only for the tropical semiring but also the arctic one.

FAQs

sparkles

AI

What defines the expressive power of weighted automata compared to neural networks?add

The research indicates that weighted automata have a distinct expressive power; for instance, certain operations on weighted automata were found decidable while equivalent operations in neural networks proved computationally complex, notably in 2020.

How do max-plus semiring concepts influence cost-register automata?add

The study reveals that the max-plus semiring introduces unique computational properties, such as resolving ambiguities in automata structures and defining restrictions leading to recognizable classes of languages, discussed extensively by Laure Daviaud in 2021.

Which recent findings elucidate the universality problem for unambiguous register automata?add

Recent findings show that unambiguous register automata maintain their universality despite complexity challenges, with significant advancements made in decoding their behavior outlined in Karin Quaas's 2021 presentation.

What unique characteristics do weighted context-free grammars exhibit over strong bimonoids?add

Weighted context-free grammars exhibit behaviors defined by two semantics that coincide under right distributive conditions; this distinction aids in identifying language transformations as of 2022.

What does the approximate simulation imply for the state reduction of fuzzy automata?add

The findings indicate that approximate simulations offer superior state reduction capabilities for fuzzy automata compared to exact simulations, which may fail to allow for any reduction at all.

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Manfred Droste

Theoretical Computer Science, 2007

Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speech-to-text processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi's and Elgot's fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with particular sentences of our weighted logic. We also consider weighted first-order logic and show that aperiodic series coincide with the first-order definable ones, if the semiring is locally finite, commutative and has some aperiodicity property.

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Lecture Notes in Computer Science, 2011

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By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata form a general and widely studied model. We define a suitable notion of a weighted first-order logic. Then we show that this weighted first-order logic and aperiodic polynomially ambiguous weighted automata have the same expressive power. Moreover, we obtain such equivalence results for suitable weighted sublogics and finitely ambiguous or unambiguous aperiodic weighted automata. Our results hold for general weight structures, including all semirings, average computations of costs, bounded lattices, and others.

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1.1 Finite Tree Automata........................ 18 1.2 The Pumping Lemma for Recognizable Tree Languages..... 26
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References (85)

  1. U. Fahrenberg, C. Johansen, G. Struth, and R. Bahadur Thapa. Generating posets beyond N. CoRR, abs/1910.06162, 2019.
  2. P. C. Fishburn. Intransitive indi↵erence with unequal indi↵erence intervals. J. Math. Psych., 7(1):144-149, 1970.
  3. H. Furusawa and G. Struth. Concurrent dynamic algebra. ACM Trans. Comput. Log., 16(4):30:1- 30:38, 2015.
  4. M. Herlihy and J. M. Wing. Linearizability: A correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst., 12(3):463-492, 1990.
  5. T. Hoare, B. Möller, G. Struth, and I. Wehrman. Concurrent Kleene algebra and its foundations. J. Log. Algebr. Program., 80(6):266-296, 2011.
  6. R. Janicki and M. Koutny. Structure of concurrency. Theor. Comput. Sci., 112(1):5-52, 1993.
  7. R. Janicki and X. Yin. Modeling concurrency with interval traces. Inf. Comput., 253:78-108, 2017.
  8. P. Jipsen and M. A. Moshier. Concurrent Kleene algebra with tests and branching automata. J. Log. Algebr. Meth. Program., 85(4):637-652, 2016.
  9. T. Kappé, P. Brunet, J. Rot, A. Silva, J. Wagemaker, and F. Zanasi. Kleene algebra with observations. In CONCUR 2019, vol. 140 of LIPIcs. Schloss Dagstuhl -Leibniz-Zentrum für Informatik, 2019.
  10. T. Kappé, P. Brunet, A. Silva, and F. Zanasi. Concurrent Kleene algebra: Free model and completeness. In ESOP 2018, vol. 10801 of LNCS. Springer, 2018.
  11. L. Lamport. The mutual exclusion problem: Part I -a theory of interprocess communication. J. ACM, 33(2):313-326, 1986.
  12. L. Lamport. On interprocess communication. Part I: basic formalism. Distributed Computing, 1(2):77-85, 1986.
  13. M. R. Laurence and G. Struth. Completeness theorems for pomset languages and concurrent Kleene algebras. CoRR, abs/1705.05896, 2017.
  14. K. Lodaya and P. Weil. Series-parallel languages and the bounded-width property. Theor. Comput. Sci., 237(1-2):347-380, 2000.
  15. D. Peleg. Concurrent dynamic logic. J. ACM, 34(2):450-479, 1987.
  16. R. J. van Glabbeek. The refinement theorem for ST-bisimulation semantics. In IFIP TC2 Working Conf. Programming Concepts and Methods. North-Holland, 1990.
  17. R. J. van Glabbeek and F. W. Vaandrager. Petri net models for algebraic theories of concurrency. In PARLE (2), vol. 259 of LNCS. Springer, 1987.
  18. W. Vogler. Failures semantics based on interval semiwords is a congruence for refinement. Dis- tributed Computing, 4:139-162, 1991.
  19. W. Vogler. Modular Construction and Partial Order Semantics of Petri Nets, vol. 625 of Lecture Notes in Computer Science. Springer, 1992.
  20. N. Wiener. A contribution to the theory of relative position. Proc. Camb. Philos. Soc., 17:441- 449, 1914.
  21. J. Winkowski. An algebraic characterization of the behaviour of non-sequential systems. Inf. Process. Lett., 6(4):105-109, 1977.
  22. Laura Banarescu, Claire Bonial, Shu Cai, Madalina Georgescu, Kira Griffitt, Ulf Herm- jakob, Kevin Knight, Philipp Koehn, Martha Palmer, and Nathan Schneider. Abstract meaning representation for sembanking. In Proc. of the 7th Linguistic Annotation Work- shop and Interoperability with Discourse, 2013.
  23. Henrik Björklund, Frank Drewes, and Petter Ericson. Parsing weighted order-preserving hyperedge replacement grammars. In Proceedings of the 16th Meeting on the Mathemat- ics of Language, pages 1-11, 2019.
  24. Annegret Habel. Hyperedge replacement: grammars and languages, volume 643. Springer Science & Business Media, 1992.
  25. Frank Drewes, Hans-Jörg Kreowski, and Annegret Habel. Hyperedge replacement graph grammars. In Handbook of Graph Grammars and Computing by Graph Transformation. 1997.
  26. Frank Drewes and Berthold Hoffmann. Contextual hyperedge replacement. Acta Infor- matica, 52(6):497-524, 2015.
  27. Frank Drewes and Anna Jonsson. Contextual hyperedge replacement grammars for abstract meaning representations. In Proceedings of the 13th International Workshop on Tree Adjoining Grammars and Related Formalisms, pages 102-111, Umeå, 2017. Association for Computational Linguistics.
  28. Frank Drewes, Berthold Hoffmann, and Mark Minas. Extending predictive shift-reduce parsing to contextual hyperedge replacement grammars. In Esther Guerra and Fernando Orejas, editors, Graph Transformation, pages 55-72, Cham, 2019. Springer International Publishing. References
  29. P. Buchholz, Bisimulation relations for weighted automata, Theoretical Computer Science, 393 (2008) 109-123.
  30. M. Ćirić, J. Ignjatović, M. Bašić, I. Jančić, Nondeterministic automata: Equivalence, bisimulations, and uniform relations, Information Sciences 261 (2014) 185 -218.
  31. M. Ćirić, J. Ignjatović, N. Damljanović, M. Bašić, Bisimulations for fuzzy automata, Fuzzy Sets and Systems 186 (2012) 100-139.
  32. N. Damljanović, M. Ćirić, J. Ignjatović, Bisimulations for weighted automata over an additively idempotent semiring, Theoretical Computer Science 534 (2014) 86-100.
  33. A. Dovier, C. Piazza, A. Policriti, An efficient algorithm for computing bisimulation equivalence, Theoretical Computer Science 311 (2004) 221-256.
  34. S. Stanimirović, I. Micić, and M. Ćirić, Approximate bisimulations for fuzzy au- tomata over complete heyting algebras, IEEE Transactions on Fuzzy Systems, 2020. doi: 10.1109/TFUZZ.2020.3039968.
  35. S. Qiao and P. Zhu. Limited approximate bisimulations and the corresponding rough approximations. International Journal of Approximate Reasoning 130 (2021) 50-82.
  36. C. Yang and Y. Li, "-bisimulation relations for fuzzy automata. IEEE Transactions on Fuzzy Systems, 26(4):2017 -2029, 2018.
  37. C. Yang and Y. Li, Approximate bisimulation relations for fuzzy automata. Soft Computing, 22(14):4535-4547, 2018.
  38. C. Yang and Y. Li. Approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures. Fuzzy Sets and Systems, 391:72-95, 2020.
  39. References
  40. Mohri, Mehryar, and Michael D. Riley. "A disambiguation algorithm for weighted automata." Theoretical Computer Science 679 (2017): 53-68.
  41. References [1] Taolue Chen and Stefan Kiefer. 2014. On the total variation distance of labelled Markov chains. In Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). ACM, 33.
  42. Dmitry Chistikov, Andrzej S. Murawski, and David Purser. 2019. Asymmetric Distances for Approximate Dierential Privacy. In 30th International Conference on Concurrency Theory, CONCUR 2019, August 27-30, 2019, Amsterdam, the Netherlands. 10:1-10:17.
  43. Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam D. Smith. 2006. Calibrating Noise to Sensitivity in Private Data Analysis. In Theory of Cryptography, Third Theory of Cryptography Conference, TCC 2006, New York, NY, USA, March 4-7, 2006, Proceedings. 265-284. hps://doi.org/10.1007/ 11681878_14
  44. Stefan Kiefer. 2018. On Computing the Total Variation Distance of Hidden Markov Models. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
  45. Serge Lang. 1966. Introduction to transcendental numbers. Addison-Wesley Pub. Co.
  46. Angus Macintyre and Alex J Wilkie. 1996. On the decidability of the real exponential eld. A K Peters, 441-467.
  47. Azaria Paz. 2014. Introduction to probabilistic automata. Academic Press.
  48. Hans Schneider. 1986. The inuence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: A survey. Linear Algebra Appl. 84 (1986), 161-189.
  49. Marcel Paul Schützenberger. 1961. On the denition of a family of automata. Information and control 4, 2-3 (1961), 245-270.
  50. Larry J Stockmeyer and Albert R Meyer. 1973. Word problems requiring exponential time (preliminary report). In Proceedings of the fth annual ACM symposium on Theory of computing. ACM, 1-9.
  51. Wen-Guey Tzeng. 1992. A polynomial-time algorithm for the equivalence of probabilistic automata. SIAM J. Comput. 21, 2 (1992), 216-227.
  52. M. Droste, S. Dziadek, W. Kuich. Greibach normal form for !-algebraic systems and weighted simple !-pushdown automata, 2020. Submitted, arXiv:2007.08866.
  53. M. Droste, S. Dziadek, W. Kuich. Greibach normal form for !-algebraic systems and weighted simple !-pushdown automata. In: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019), LIPIcs, vol. 150, pp. 38:1-38:14, 2019. doi:10.4230/LIPIcs.FSTTCS.2019.38.
  54. B. Borchardt, Z. Fülöp, Z. Gazdag, and A. Maletti. Bounds for tree automata with polynomial costs. J. Autom. Lang. Comb., 10:107-157, 2005.
  55. B. Borchardt and H. Vogler. Determinization of finite state weighted tree automata. J. Autom. Lang. Comb., 8(3):417-463, 2003.
  56. M. Ćirić, M. Droste, J. Ignjatović, and H. Vogler. Determinization of weighted finite automata over strong bimonoids. Inf. Sci., 180(18):3479-3520, 2010.
  57. M. Droste, Z. Fülöp, D. Kószó, and H. Vogler. Crisp-Determinization of Weighted Tree Automata over Additively Locally Finite and Past-Finite Monotonic Strong Bimonoids Is Decidable. G. Jirásková and G. Pighizzini (Eds.): DCFS 2020, LNCS 12442, pp. 39-51, 2020.
  58. M. Droste, T. Stüber, and H. Vogler. Weighted finite automata over strong bimonoids. Inf. Sci., 180(1):156-166, 2010.
  59. Z. Fülöp, D. Kószó, and H. Vogler. Crisp-determinization of weighted tree automata over strong bimonoids. see also: arXiv:1912.02660v2 [cs.FL] 2 Feb 2021.
  60. J. A. Goguen, J. W. Thatcher, E. G. Wagner, and J. B. Wright. "Initial Algebra Semantics and Continuous Algebras". In: Journal of the Association for Computational Machinery (1977).
  61. W. Kuich. "Linear systems of equations and automata on distributive multioperator monoids". In: Contributions to general algebra (1999).
  62. M. Mohri. "Semiring frameworks and algorithms for shortest-distance problems". In: Journal of Automata, Languages and Combinatorics (2002).
  63. J. Goodman. "Semiring parsing". In: Computational Linguistics (1999).
  64. M.-J. Nederhof. "Weighted deductive parsing and Knuth's algorithm". In: Computational Linguistics (2003).
  65. R. Giegerich, C. Meyer, and P. Ste↵en. "A discipline of dynamic programming over sequence data". In: Science of Computer Programming (2004).
  66. Ćirić M, Ignjatović J, Bašić M, Jančić I (2014) Nondeterministic automata: equiv- alence, bisimulations, and uniform relations. Inf Sci 261:185-218
  67. Ćirić M, Ignjatović J, Damljanović N, Bašić M (2012) Bisimulations for fuzzy au- tomata. Fuzzy Sets Syst 186:100-139
  68. Ćirić M, Ignjatović J, Jančić I, Damljanović N (2012) Computation of the greatest simulations and bisimulations between fuzzy automata. Fuzzy Sets Syst 208:22-42
  69. Damljanović N, Ćirić M, Ignjatović, J (2014) Bisimulations for weighted automata over an additively idempotent semiring. Theor Comput Sci 534:86-100
  70. Ignjatović J, Ćirić M (2012) Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey. Filomat 26(2):207-241
  71. Ignjatović J, Ćirić M, Bogdanović S (2010) On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations. Fuzzy Sets Syst 161:3081-3113
  72. Ignjatović J, Ćirić M, Damljanović N, Jančić I (2012) Weakly linear systems of fuzzy relation inequalities: The heterogeneous case. Fuzzy Sets Syst 199:64-91
  73. Jančić Z, Micić I, Ignjatović J, Ćirić M (2016) Further improvements of determiniza- tion methods for fuzzy finite automata. Fuzzy Sets Syst 301:79-102
  74. Ćirić M, Stamenković A, Ignjatović J, Petković T (2007) Factorization of fuzzy automata. in: E. Csuhaj-Varju, and Z. Ésik (eds.), FCT 2007, Lecture Notes in Computer Science 4639:213-225
  75. Ćirić M, Stamenković A, Ignjatović J, Petković T (2010) Fuzzy relation equations and reduction of fuzzy automata. J Comput Syst Sci 76:609-633
  76. Stamenković A, Ćirić M, Bašić M (2018) Ranks of fuzzy matrices. Applications in state reduction of fuzzy automata. Fuzzy Sets Syst 333:124-139
  77. Stamenković A, Ćirić M, Ignjatović J (2014) Reduction of fuzzy automata by means of fuzzy quasi-orders. Inf Sci 275:168-198
  78. M. Ćirić, M. Droste, J. Ignjatović, H. Vogler, Determinization of weighted finite automata over strong bimonoids, Information Sciences 180 (2010) 3497-3520.
  79. M. Droste, T. Stüber, H. Vogler, Weighted finite automata over strong bimonoids, Information Sciences 180 (2010) 156-166.
  80. M. Droste, H. Vogler, The Chomsky-Schtzenberger theorem for quantitative context-free languages, Internat. J. Found. Comput. Sci. 25 (2014) 955-969.
  81. Z. Ésik, W. Kuich, Modern automata theory, http://www.dmg .tuwien .ac .at /kuich, 2007.
  82. J. H. Jin, C. Q. Li, The algebraic characterizations for a formal power series over complete strong bimonoids, Springer Plus 5 (2016) Article no. 310.
  83. W. Kuich, A. Salomaa, Semirings, Automata, Languages, Monogr. Theoret. Com- put. Sci. EATCS Ser., vol.5, Springer, 1986.
  84. G. Rahonis, F. Torpari, Weighted context-free grammars over bimonoids, Scientific Annals of Computer Science 29 (1) (2019) 59-80.
  85. Y. Shang, X. Lu, R. Lu, A theory of computation based on unsharp quantum logic: Finite state automata and pushdown automata, Theoretical Computer Science 434 (2012) 53-86.

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