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A Burnside Approach to the Termination of Mohri's Algorithm for Polynomially Ambiguous Min-Plus-Automata

Published online by Cambridge University Press:  03 June 2008

Daniel Kirsten
Daniel Kirsten*
Affiliation:
Universität Leipzig, Institut für Informatik, Postfach 10 09 20, 04009 Leipzig, Germany
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Abstract

We show that the termination of Mohri's algorithm is decidable for polynomially ambiguous weighted finite automata over the tropical semiring which gives a partial answer to a question by Mohri [29]. The proof relies on an improvement of the notion of the twins property and a Burnside type characterization for the finiteness of the set of states produced by Mohri's algorithm.

Keywords

Weighted automatatropical semiringdeterminization.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 553 - 581
Copyright
© EDP Sciences, 2008

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References

C. Allauzen and M. Mohri, Efficient algorithms for testing the twins property. Journal of Automata, Languages and Combinatorics 8 (2003) 117–144.
J. Berstel and C. Reutenauer, Rational Series and Their Languages, volume 12 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, Berlin Heidelberg New York (1984).
A.L. Buchsbaum, R. Giancarlo and J.R. Westbrook, On the determinization of weighted finite automata. SIAM Journal of Computing (2000) 1502–1531.
Chalopin, J. and Leung, H., A note on factorization forests of finite height. Theoretical Computer Science 310 (2004) 489–499. CrossRef
Choffrut, C., Une caracterisation des fonctions sequentielles et des fonctions sous-sequentielles en tant que relations rationnelles. Theoretical Computer Science 5 (1977) 325–337. CrossRef
Culik II, K. and Kari, J., Image compression using weighted finite automata. Computer and Graphics 17 (1993) 305–313. CrossRef
G. Grahne and A. Thomo, Approximate reasoning in semi-structured databases. In 8th International Workshop on Knowledge Representation meets Databases (KRDB2001), M. Lenzerini et al., Eds. volume 45 of CEUR Workshop Proceedings (2001).
U. Hafner, Low Bit-Rate Image and Video Coding with Weighted Finite Automata. PhD thesis, Universität Würzburg (1999).
Hashiguchi, K., Algorithms for determining relative star height and star height. Information and Computation 78 (1988) 124–169. CrossRef
Hashiguchi, K., Improved limitedness theorems on finite automata with distance functions. Theoretical Computer Science 72 (1990) 27–38. CrossRef
Hashiguchi, K., New upper bounds to the limitedness of distance automata. Theoretical Computer Science 233 (2000) 19–32. CrossRef
Hashiguchi, K., Ishiguro, K. and Jimbo, S., Decidability of the equivalence problem for finitely ambiguous finance automata. International Journal of Algebra and Computation 12 (2002) 445–461. CrossRef
J. Hromkovič, J. Karhumäki, H. Klauck, G. Schnitger and S. Seibert, Measures of nondeterminism in finite automata. In ICALP'00 Proceedings, volume 1853 of Lecture Notes in Computer Science, U. Montanari et al., Eds. pages 199–210. Springer-Verlag, Berlin (2000).
Hromkovič, J., Karhumäki, J., Klauck, H., Schnitger, G. and Seibert, S., Communication complexity method for measuring nondeterminism in finite automata. Information and Computation 172 (2002) 202–217. CrossRef
O. Ibarra and B. Ravikumar, On sparseness, ambiguity and other decision problems for acceptors and transducers. In STACS'86 Proceedings, volume 210 of Lecture Notes in Computer Science, B. Monien and G. Vidal-Naquet, Eds. pages 171–179. Springer-Verlag, Berlin (1986).
Z. Jiang, B. Litov and O. de Vel, Similarity enrichments in image compression through weighted finite automata. In COCOON'00 Proceedings, volume 1858 of Lecture Notes in Computer Science, pages 447–456. Springer-Verlag, Berlin (2000).
F. Katritzke, Refinements of Data Compression using Weighted Finite Automata. PhD thesis, Universität Siegen (2001).
Kirsten, D., Distance desert automata and the star height problem. RAIRO-Theor. Inf. Appl. 39 (2005) 455–509. CrossRef
D. Kirsten and I. Mäurer, On the determinization of weighted automata. Journal of Automata, Languages and Combinatorics 10 (2005) 287–312.
Klimann, I., Lombardy, S., Mairesse, J. and Prieur, C., Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton. Theoretical Computer Science 327 (2004) 349–373. CrossRef
Krob, D., The equality problem for rational series with multiplicities in the tropical semiring is undecidable. International Journal of Algebra and Computation 4 (1994) 405–425. CrossRef
W. Kuich, Semirings and formal power series. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, Vol. 1, Word, Language, Grammar, pages 609–677. Springer-Verlag, Berlin (1997).
W. Kuich and A. Salomaa, editors. Semirings, Automata, Languages, volume 5 of Monographs in Theoretical Computer Science. An EATCS Series. Springer-Verlag, Berlin (1986).
Leung, H., Limitedness theorem on finite automata with distance functions: An algebraic proof. Theoretical Computer Science 81 (1991) 137–145. CrossRef
Leung, H., Separating exponentially ambiguous finite automata from polynomially ambiguous finite automata. SIAM Journal of Computing 27 (1998) 1073–1082. CrossRef
H. Leung, The topological approach to the limitedness problem on distance automata. In J. Gunawardena, editor, Idempotency, pages 88–111. Cambridge University Press (1998).
Leung, H. and Podolskiy, V., The limitedness problem on distance automata: Hashiguchi's method revisited. Theoretical Computer Science 310 (2004) 147–158. CrossRef
Métivier, Y. and Richomme, G., New results on the star problem in trace monoids. Information and Computation 119 (1995) 240–251. CrossRef
Mohri, M., Finite-state transducers in language and speech processing. Computational Linguistics 23 (1997) 269–311.
A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs on Computer Science. Springer-Verlag, Berlin Heidelberg New York (1978).
I. Simon, Recognizable sets with multiplicities in the tropical semiring. In M. P. Chytil et al., editors, MFCS'88 Proceedings, volume 324 of Lecture Notes in Computer Science, pages 107–120. Springer-Verlag, Berlin (1988).
Simon, I., Factorization forests of finite height. Theoretical Computer Science 72 (1990) 65–94. CrossRef
I. Simon, A short proof of the factorization forest theorem. In M. Nivat and A. Podelski, Eds. Tree Automata and Languages, pages 433–438. Elsevier Science Publishers B.V. (1992).
Simon, I., On semigroups of matrices over the tropical semiring. RAIRO-Theor. Inf. Appl. 28 (1994) 277–294. CrossRef
Weber, A., Distance automata having large finite distance or finite ambiguity. Mathematical Systems Theory 26 (1993) 169–185. CrossRef
Weber, A., Finite valued distance automata. Theoretical Computer Science 134 (1994) 225–251. CrossRef