Abstract
Leftist grammars can be characterized in terms of rules of the form a→ ba and cd→ d, without distinction between terminals and nonterminals. They were introduced by Motwani et. al. [9] , where the accessibility problem for some general protection system was related to the membership problem of these grammars. This protection system was originally proposed in [3,10] in the context of Java virtual worlds. We show that the set of languages defined by general leftist grammars is not included in CFL, answering in negative a question from [9]. Moreover, we relate some restricted but naturally defined variants of leftist grammars to the language classes of the Chomsky hierarchy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blaze, M., Feigenbaum, J., Ioannidis, J., Keromytis, A.: The role of trust management in distributed security. In: Vitek, J. (ed.) Secure Internet Programming. LNCS, vol. 1603, pp. 185–210. Springer, Heidelberg (1999)
Budd, T.: Safety in grammatical protection systems. International Journal of Computer and Information Sciences 12(6), 413–430 (1983)
Cheiner, O., Saraswat, V.: Security Analysis of Matrix. Technical report, AT&T Shannon Laboratory (1999)
Harrison, M.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)
Harrison, M., Ruzzo, W., Ullman, J.: Protection in operating systems. Communications of the ACM 19(8), 461–470 (1976)
Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (2000)
Lipton, R., Budd, T.: On Classes of Protection Systems. In: Foundations of Secure Computation, pp. 281–296. Academic Press, London (1978)
Lipton, R., Snyder, L.: A linear time algorithm for deciding subject security. Journal of the ACM 24(3), 455–464 (1977)
Motwani, R., Panigrahy, R., Saraswat, V., Venkatasubramanian, S.: On the decidability of accessibility problems (extended abstract). In: STOC 2000, pp. 306–315 (2000)
Saraswat, V.: The Matrix Design. Technical report, AT&T Laboratory (April 1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jurdziński, T., Loryś, K. (2005). Leftist Grammars and the Chomsky Hierarchy. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_26
Download citation
DOI: https://doi.org/10.1007/11537311_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28193-1
Online ISBN: 978-3-540-31873-6
eBook Packages: Computer ScienceComputer Science (R0)