Abstract
The Parikh matrix mapping is a concept that provides information on the number of occurrences of certain (scattered) subwords in a word. Although Parikh matrices have been thoroughly studied, many of their basic properties remain open. In the present paper, we describe a toolkit that has been developed to support research in this field. Its functionality includes elementary and advanced operations related to Parikh matrices and the recently introduced variants of \(\mathbb {P}\)-Parikh matrices and \(\mathbb {L}\)-Parikh matrices.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The software is implemented in Java, it is open-source and has been made available under the MIT License. It is available online at www.github.com/LHutch1/Parikh-Matrices-Toolkit.
- 2.
References
Alazemi, H.M.K., Černý, A.: Several extensions of the Parikh matrix L-morphism. J. Comput. Syst. Sci. 79, 658–668 (2013)
Atanasiu, A.: Parikh matrix mapping and amiability over a ternary alphabet. In: Discrete Mathematics and Computer Science in Memoriam Alexandru Mateescu (1952–2005), pp. 1–12 (2014)
Atanasiu, A., Atanasiu, R., Petre, I.: Parikh matrices and amiable words. Theoret. Comput. Sci. 390, 102–109 (2008)
Atanasiu, A., Martín-Vide, C., Mateescu, A.: On the injectivity of the Parikh matrix mapping. Fund. Inform. 49, 289–299 (2002)
Atanasiu, A., Teh, W.C.: A new operator over Parikh languages. Int. J. Found. Comput. Sci. 27, 757–769 (2016)
Bera, S., Mahalingam, K.: Some algebraic aspects of Parikh q-matrices. Int. J. Found. Comput. Sci. 27, 479–500 (2016)
Dick, J., Hutchinson, L.K., Mercaş, R., Reidenbach, D.: Reducing the ambiguity of Parikh matrices. Theoret. Comput. Sci. 860, 23–40 (2021)
Duval, J.P.: Factorizing words over an ordered alphabet. J. Algorithms 4, 363–381 (1983)
Egecioglu, O., Ibarra, O.H.: A matrix Q-analogue of the Parikh map. In: Levy, J.-J., Mayr, E.W., Mitchell, J.C. (eds.) TCS 2004. IIFIP, vol. 155, pp. 125–138. Springer, Boston (2004). https://doi.org/10.1007/1-4020-8141-3_12
Fossé, S., Richomme, G.: Some characterizations of Parikh matrix equivalent binary words. Inf. Process. Lett. 92, 77–82 (2004)
Hall, B.C.: Lie Groups, Lie Algebras, and Representations. GTM, vol. 222. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-13467-3
Lejeune, M., Rigo, M., Rosenfeld, M.: On the binomial equivalence classes of finite words. Int. J. Algebra Comput. 30, 1375–1397 (2020)
Mahalingam, K., Subramanian, K.G.: Product of Parikh matrices and commutativity. Int. J. Found. Comput. Sci. 23, 207–223 (2012)
Mateescu, A., Salomaa, A.: Matrix indicators for subword occurrences and ambiguity. Int. J. Found. Comput. Sci. 15, 277–292 (2004)
Mateescu, A., Salomaa, A., Salomaa, K., Yu, S.: On an extension of the Parikh mapping. Turku Centre for Computer Science (2000)
Mateescu, A., Salomaa, A., Salomaa, K., Yu, S.: A sharpening of the Parikh mapping. RAIRO-Theor. Inf. Appl. 35, 551–564 (2001)
Parikh, R.J.: On context-free languages. J. ACM 13, 570–581 (1966)
Poovanandran, G., Chean Teh, W.: Strong (2\(\cdot \)t) and strong (3\(\cdot \)t) transformations for strong M-equivalence. Int. J. Found. Comput. Sci. 30, 719–733 (2019)
Salomaa, A., Yu, S.: Subword occurrences, Parikh matrices and Lyndon images. Int. J. Found. Comput. Sci. 21, 91–111 (2010)
Şerbănuţă, T.F.: Extending Parikh matrices. Theoret. Comput. Sci. 310, 233–246 (2004)
Şerbănuţă, V.N.: On Parikh matrices, ambiguity, and prints. Int. J. Found. Comput. Sci. 20, 151–165 (2009)
Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13, 354–356 (1969)
Acknowledgements
The authors wish to thank the anonymous referees for their thorough and helpful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Hutchinson, L.K., Mercaş, R., Reidenbach, D. (2022). A Toolkit for Parikh Matrices. In: Caron, P., Mignot, L. (eds) Implementation and Application of Automata. CIAA 2022. Lecture Notes in Computer Science, vol 13266. Springer, Cham. https://doi.org/10.1007/978-3-031-07469-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-07469-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-07468-4
Online ISBN: 978-3-031-07469-1
eBook Packages: Computer ScienceComputer Science (R0)