Abstract
We give an answer to a fundamental question, raised by Konstantinidis, Santean, and Yu [Acta Inform. 43 (2007) 395–417], of whether all multi-valued partial CFL functions can be refined by single-valued partial CFL functions. We negatively solve this question by presenting a special multi-valued partial CFL function as an example function and by proving that no refinement of this particular function becomes a single-valued partial CFL function. This contrasts an early result of Kobayashi [Inform. Control 15 (1969) 95–109] that multi-valued partial NFA functions are always refined by single-valued NFA functions. Our example function turns out to be unambiguously 2-valued, and thus we obtain a stronger separation result, in which no refinement of unambiguously 2-valued partial CFL functions can be single-valued. Our proof consists of manipulations and close analyses of underlying one-way one-head nondeterministic pushdown automata equipped with write-only output tapes.
Chapter PDF
Similar content being viewed by others
Keywords
References
Choffrut, C., Culik, K.: Properties of finite and pushdown transducers. SIAM J. Comput. 12, 300–315 (1983)
Evey, R.J.: Application of pushdown-store machines. In: Proc. 1963 Fall Joint Computer Conference, pp. 215–227. AFIPS Press (1963)
Fisher, P.C.: On computability by certain classes of restricted Turing machines. In: Proc. 4th Annual IEEE Symp. on Switching Circuit Theory and Logical Design (SWCT 1963), pp. 23–32. IEEE Computer Society (1963)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley (2001)
Kobayashi, K.: Classification of formal langauges by functional binary transductions. Inform. Control 15, 95–109 (1969)
Konstantinidis, S., Santean, N., Yu, S.: Representation and uniformization of algebraic transductions. Acta Inform. 43, 395–417 (2007)
Selman, A.L.: A taxonomy of complexity classes of functions. J. Comput. System Sci. 48, 357–381 (1994)
Selman, A.L.: Much ado about functions. In: Proc. of the 11th Annual IEEE Conference on Computational Complexity, pp. 198–212 (1996)
Tadaki, K., Yamakami, T., Lin, J.C.H.: Theory of one-tape linear-time Turing machines. Theoret. Comput. Sci. 411, 22–43 (2010)
Yamakami, T.: Swapping lemmas for regular and context-free languages (2008), Available at arXiv:0808.4122
Yamakami, T.: Pseudorandom generators against advised context-free languages (2009), See arXiv:0902.2774
Yamakami, T.: Immunity and pseudorandomness of context-free languages. Theor. Comput. Sci. 412, 6432–6450 (2011)
Yamakami, T.: Oracle pushdown automata, nondeterministic reducibilities, and the hierarchy over the family of context-free languages. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds.) SOFSEM 2014. LNCS, vol. 8327, pp. 514–525. Springer, Heidelberg (2014)
Yamakami, T.: Structural complexity of multi-valued partial functions computed by nondeterministic pushdown automata (2014) (unpublished manuscript)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 IFIP International Federation for Information Processing
About this paper
Cite this paper
Yamakami, T. (2014). Not All Multi-Valued Partial CFL Functions Are Refined by Single-Valued Functions (Extended Abstract). In: Diaz, J., Lanese, I., Sangiorgi, D. (eds) Theoretical Computer Science. TCS 2014. Lecture Notes in Computer Science, vol 8705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44602-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-662-44602-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44601-0
Online ISBN: 978-3-662-44602-7
eBook Packages: Computer ScienceComputer Science (R0)