Skip to main content

Algorithms and Training for Weighted Multiset Automata and Regular Expressions

  • Conference paper
  • First Online:
  • 353 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10977))

Abstract

Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present training methods to learn the weights for weighted regular expressions and for general multiset automata from data. Finally, we examine situations in which inside weights can be computed more efficiently.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Barría, J., Halmos, P.R.: Vector bases for two commuting matrices. Linear and Multilinear Algebra 27, 147–157 (1990)

    Article  MathSciNet  Google Scholar 

  2. Berry, G., Sethi, R.: From regular expressions to deterministic automata. Theor. Comput. Sci. 48, 117–126 (1986)

    Article  MathSciNet  Google Scholar 

  3. Chiang, D., Drewes, F., Lopez, A., Satta, G.: Weighted DAG automata for semantic graphs. Comput. Linguist. 44, 119–186 (2018)

    Article  MathSciNet  Google Scholar 

  4. Droste, M., Gastin, P.: The Kleene-Schützenberger theorem for formal power series in partially commuting variables. Inf. Comput. 153, 47–80 (1999)

    Article  Google Scholar 

  5. Gerstenhaber, M.: On dominance and varieties of commuting matrices. Ann. Math. 73(2), 324–348 (1961)

    Article  MathSciNet  Google Scholar 

  6. Harary, F.: The determinant of the adjacency matrix of a graph. SIAM Rev. 4(3), 202–210 (1962)

    Article  MathSciNet  Google Scholar 

  7. Holbrook, J., O’Meara, K.C.: Some thoughts on Gerstenhaber’s theorem. Linear Algebra Appl. 466, 267–295 (2015)

    Article  MathSciNet  Google Scholar 

  8. Johnson, D.B.: Finding all the elementary circuits of a directed graph. SIAM J. Comput. 4(1), 77–84 (1975)

    Article  MathSciNet  Google Scholar 

  9. Ladner, R.E., Fischer, M.J.: Parallel prefix computation. J. ACM (JACM) 27(4), 831–838 (1980)

    Article  MathSciNet  Google Scholar 

  10. Rutherford, D.E.: The Cayley-Hamilton theorem for semi-rings. Proc. Roy. Soc. Edinb. 66(4), 211–215 (1964)

    MathSciNet  MATH  Google Scholar 

  11. Thomassen, C.: On digraphs with no two disjoint directed cycles. Combinatorica 7(1), 145–150 (1987)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank the anonymous reviewers for their very detailed and helpful comments.

This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via AFRL Contract #FA8650-17-C-9116. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Justin DeBenedetto .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

DeBenedetto, J., Chiang, D. (2018). Algorithms and Training for Weighted Multiset Automata and Regular Expressions. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94812-6_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94811-9

  • Online ISBN: 978-3-319-94812-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics