Abstract
We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters. We show that, while most codes populate the lower region approximating a superposition of Thomae functions, there is a substantial presence of codes above the Gilbert–Varshamov bound and even above the asymptotic bound and the Plotkin bound. We investigate the dynamics induced on the space of code parameters by spin glass models of language change, and show that, in the presence of entailment relations between syntactic parameters the dynamics can sometimes improve the code. For large sets of languages and syntactic data, one can gain information on the spin glass dynamics from the induced dynamics in the space of code parameters.
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References
Baker, M.: The Atoms of Language. Basic Books, New York (2001)
Barg, A., Forney, G.D.: Random codes: minimum distances and error exponents. IEEE Trans. Inf. Theory 48(9), 2568–2573 (2002)
Chomsky, N.: Lectures on Government and Binding. Foris Publications, Dordrecht (1982)
Chomsky, N., Lasnik, H.: The theory of Principles and Parameters, in “Syntax: An international handbook of contemporary research”, pp. 506–569, de Gruyter (1993)
Coffey, J.T., Goodman, R.M.: Any code of which we cannot think is good. IEEE Trans. Inf. Theory 36(6), 1453–1461 (1990)
Longobardi, G., Guardiano, C.: Evidence for syntax as a signal of historical relatedness. Lingua 119, 1679–1706 (2009)
Longobardi, G., Guardiano, C., Silvestri, G., Boattini, A., Ceolin, A.: Towards a syntactic phylogeny of modern Indo-European languages. J. Hist. Linguist. 3(1), 122–152 (2013)
Manin, Y.I.: What is the maximum number ofpoints on a curve over \({\mathbb{F}}_2\)? J. Fac. Sci. Univ. Tokyo Sect. IA Math 2(83), 715–720 (1982)
Manin, Y.I.: A computability challenge: asymptotic bounds and isolated error-correcting codes, in “Computation, physics and beyond”, pp. 174–182, Lecture Notes in Comput. Sci., vol. 7160, Springer (2012)
Manin, Y.I.: Complexity vs Energy: Theory of Computation and Theoretical Physics, arXiv:1302.6695 [cs.CC]
Manin, Y.I., Marcolli, M.: Error-correcting codes and phase transitions. Math. Comput. Sci. 5, 133–170 (2011)
Manin, YuI, Marcolli, M.: Kolmogorov complexity and the asymptotic bound for error-correcting codes. J. Differ. Geom. 97, 91–108 (2014)
Marcolli, M.: Syntactic parameters and a coding theory perspective on entropy and complexity of language families. Entropy 18(4), 110 (2016)
Park, J.J., Boettcher, R., Zhao, A., Mun, A., Yuh, K., Kumar, V., Marcolli, M.: Prevalence and recoverability of syntactic parameters in sparse distributed memories, arXiv:1510.06342 [cs.CL]
Port, A., Gheorghita, I., Guth, D., Clark, J.M., Liang, C., Dasu, S., Marcolli, M.: Persistent Topology of Syntax, arXiv:1507.05134 [cs.CL]
Ronen, S., Goncalves, B., Hu, K.Z., Vespignani, A., Pinker, S., Hidalgo, C.A.: Links that speak: the global language network and its association with global fame. Proc. Natl. Acad. Sci. 111(52), E5616–E5622 (2014)
Siva, K., Tao, J., Marcolli, M.: Spin Glass Models of Syntax and Language Evolution, arXiv:1508.00504 [cs.CL]
Tsfasman, M.A., Vladut, S.G.: Algebraic-geometric codes, Mathematics and its Applications (Soviet Series), vol. 58, Kluwer Academic Publishers (1991)
Tsfasman, M.A., Vladut, S.G., Zink, T.: Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound. Math. Nachr. 109, 21–28 (1982)
Vladut, S.G., Drinfeld, V.G.: The number of points of an algebraic curve. Funktsional. Anal. I Prilozhen. 17(1), 68–69 (1983)
SSWL Database of Syntactic Parameters: http://sswl.railsplayground.net/
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Shu, K., Marcolli, M. Syntactic Structures and Code Parameters. Math.Comput.Sci. 11, 79–90 (2017). https://doi.org/10.1007/s11786-017-0298-0
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DOI: https://doi.org/10.1007/s11786-017-0298-0
Keywords
- Natural languages
- Syntactic parameters
- Error-correcting codes
- Code parameters
- Asymptotic bounds
- Spin glass dynamics