Abstract
In each grammar model, it is an important question whether erasing productions are necessary to generate all languages. Using the concept of grammars with control languages by Salomaa, which offers a uniform treatment of a variety of grammar models, we present a condition on the class of control languages that guarantees that erasing productions are avoidable in the resulting grammar model. On the one hand, this generalizes the previous result that in Petri net controlled grammars, erasing productions can be eliminated. On the other hand, it allows us to infer that the same is true for vector grammars.
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.
Similar content being viewed by others
References
Aho, A.V.: Indexed grammars—an extension of context-free grammars. Journal of the ACM 15, 647–671 (1968)
Cremers, A.B., Mayer, O.: On matrix languages. Information and Control 23(1), 86–96 (1973)
Dassow, J., Păun, G.: Regulated rewriting in formal language theory. Springer, Berlin (1989)
Dassow, J., Păun, G., Salomaa, A.: Grammars with controlled derivations. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 2, pp. 101–154. Springer, Berlin (1997)
Dassow, J., Turaev, S.: Petri net controlled grammars: the case of special petri nets. Journal of Universal Computer Science 15(14), 2808–2835 (2009)
Dassow, J., Turaev, S.: Petri net controlled grammars: the power of labeling and final markings. Romanian Journal of Information Science and Technology 12(2), 191–207 (2009)
Fernau, H., Stiebe, R.: Sequential grammars and automata with valences. Theoretical Computer Science 276, 377–405 (2002)
Ginsburg, S., Spanier, E.H.: Control sets on grammars. Mathematical Systems Theory 2(2), 159–177 (1968)
Salomaa, A.: On grammars with restricted use of productions. Annales Academiæ Scientiarum Fennicæ. Series A I. Mathematica 454 (1969)
Zetzsche, G.: On erasing productions in random context grammars. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 175–186. Springer, Heidelberg (2010)
Zetzsche, G.: Toward understanding the generative capacity of erasing rules in matrix grammars. International Journal of Foundations of Computer Science 22, 411–426 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zetzsche, G. (2011). A Sufficient Condition for Erasing Productions to Be Avoidable. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-22321-1_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22320-4
Online ISBN: 978-3-642-22321-1
eBook Packages: Computer ScienceComputer Science (R0)