Abstract
We look at NFAs augmented with multiple reversal-bounded counters where, during an accepting computation, the behavior of the counters during increasing and decreasing phases is specified by some fixed “pattern”. We consider families of languages defined by various pattern behaviors and show that some correspond to the smallest full trios containing restricted classes of bounded semilinear languages. For example, one such family is exactly the smallest full trio containing all the bounded semilinear languages. Another family is the smallest full trio containing all the bounded context-free languages. Still another is the smallest full trio containing all bounded languages whose Parikh map is a semilinear set where all periodic vectors have at most two non-zero coordinates. We also examine relationships between the families.
Keywords
The research of O. H. Ibarra was supported, in part, by NSF Grant CCF-1117708. The research of I. McQuillan was supported, in part, by Natural Sciences and Engineering Research Council of Canada Grant 327486-2010.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
There is a fixed c such that the number of times the boundary between any two adjacent input cells is crossed is at most c.
References
Breveglieri, L., Cherubini, A., Citrini, C., Reghizzi, S.: Multi-push-down languages and grammars. Int. J. Found. Comput. Sci. 7(3), 253–291 (1996)
Ginsburg, S.: Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland Publishing Company, Amsterdam (1975)
Ginsburg, S.: The Mathematical Theory of Context-Free Languages. McGraw-Hill Inc., New York (1966)
Greibach, S.: Remarks on blind and partially blind one-way multicounter machines. Theoret. Comput. Sci. 7, 311–324 (1978)
Harju, T., Ibarra, O., Karhumäki, J., Salomaa, A.: Some decision problems concerning semilinearity and commutation. J. Comput. Syst. Sci. 65(2), 278–294 (2002)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, MA (1979)
Ibarra, O.H., McQuillan, I.: On bounded semilinear languages, counter machines, and finite-index ET0L. In: Han, Y.-S., Salomaa, K. (eds.) CIAA 2016. LNCS, vol. 9705, pp. 138–149. Springer, Heidelberg (2016). doi:10.1007/978-3-319-40946-7_12
Ibarra, O., McQuillan, I.: On families of full trios containing counter machine languages. Technical Report 2016–01, University of Saskatchewan (2016). http://www.cs.usask.ca/documents/technical-reports/2016/TR-2016-01.pdf
Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. ACM 25(1), 116–133 (1978)
Ibarra, O.H., Seki, S.: Characterizations of bounded semilinear languages by one-way and two-way deterministic machines. Int. J. Found. Comput. Sci. 23(6), 1291–1306 (2012)
Kortelainen, J., Salmi, T.: There does not exist a minimal full trio with respect to bounded context-free languages. In: Mauri, G., Leporati, A. (eds.) DLT 2011. LNCS, vol. 6795, pp. 312–323. Springer, Heidelberg (2011)
Rozenberg, G., Vermeir, D.: On ET0L systems of finite index. Inf. Control 38, 103–133 (1978)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ibarra, O.H., McQuillan, I. (2016). On Families of Full Trios Containing Counter Machine Languages. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-662-53132-7_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53131-0
Online ISBN: 978-3-662-53132-7
eBook Packages: Computer ScienceComputer Science (R0)