Abstract
We investigate concatenation theories for some classes of one-symbol languages. These classes can be the class of all languages, the class of regular languages, or the class of finite languages. We prove that all such theories are undecidable. The last two theories are algorithmically equivalent to elementary arithmetic. The first is equivalent to second order arithmetic.
Similar content being viewed by others
REFERENCES
G. Boolos, J. P. Burgess, and R. C. Jeffrey, Computability and Logic (Cambridge Univ. Press, Cambridge, 2002).
S. M. Dudakov and B. N. Karlov, ‘‘On decidability of regular languages theories,’’ Lect. Notes Comput. Sci. 11532, 119–130 (2019).
A. Grzegorczyk, ‘‘Undecidability without arithmetization,’’ Studia Logica 79, 163–230 (2005).
A. Grzegorczyk and K. Zdanowski, ‘‘Undecidability and Concatenation,’’ in Andrzej Mostowski and Foundational Studies, Ed. by A. Ehrenfeucht, V. W. Marek, and M. Srebrny (IOS, Amsterdam, 2008), pp. 72–91.
J. E. Hopcroft, R. Motwani, and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, 3rd ed. (Pearson, Harlow, Essex, 2013).
H. Rogers, Theory of Recursive Functions and Effective Computability (McGraw-Hill Education, New York, 1967).
V. Švejdar, ‘‘On interpretability in the theory of concatenation,’’ Notre Dame J. Formal Logic 50, 87–95 (2009).
A. Visser, ‘‘Growing commas. A study of sequentiality and concatenation,’’ Notre Dame J. Formal Logic 50, 61–85 (2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dudakov, S.M. On Undecidability of Concatenation Theory for One-Symbol Languages. Lobachevskii J Math 41, 168–175 (2020). https://doi.org/10.1134/S1995080220020055
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080220020055