Summary
We study the relationship between scattered and context-sensitive rewriting. We prove that an extended version of scattered grammars produces exactly the context-sensitive languages. Also unordered scattered context languages are a proper subset of scattered context languages, and unordered scattered rewriting with erasing does not generate all scattered context (and thus not all context-sensitive) languages.
Similar content being viewed by others
References
Cremers, A.B.: Normal Forms for Context-Sensitive Grammars. Acta Inf. 3, 59–73 (1973)
Dahlhaus, E., Gaifman, H.: Concerning 2-Adjacent Context-Free Languages. Theor. Comput. Sci. 41, 169–184 (1985)
Dahlhaus, E., Warmuth, M.K.: Membership for Growing Context-Sensitive Languages is Polynomial. J. Comput. Syst. Sci. 33, 456–472 (1986)
Greibach, S., Hopcroft, J.: Scattered Context Grammars. J. Comput. Syst. Sci. 3, 233–247 (1969)
Gonczarowski, J., Shamir, E.: Pattern Selector Grammars and Several Parsing Algorithms in the Context-Free Style. J. Comput. Syst. Sci. 30, 249–273 (1985)
Gonczarowski, J., Warmuth, M.K.: Applications of Scheduling Theory to Formal Language Theory. Theor. Comput. Sci. 37, 217–243 (1985)
Gonczarowski, J., Warmuth, M.K.: Manipulating Derivation Forests by Scheduling Techniques. Theor. Comput. Sci. 45, 87–119 (1986)
Harrison, M.A.: Introduction to Formal Language Theory. Reading, MA: Addison-Wesley 1978
Kosaraju, S.R.: Decidability of Reachability in Vector Addition Systems. Proc. 14th ACM Symp. on Theory of Computing (1982), pp. 267–281
Kuroda, S.-Y.: Classes of Languages and Linear Bounded Automata. Inf. Control 6, 131–136 (1963)
Kleijn, H.C.M., Rozenberg, G.: Context-Free Like Restrictions on Selective Rewriting. Theor. Comput. Sci. 16, 237–269 (1981)
Mayr, E.W.: An Algorithm for the General Petri Net Reachability Problem. SIAM J. Comput. 13, 441–460 (1984)
Salomaa, A.: Formal Languages. New York: Academic Press 1973
Author information
Authors and Affiliations
Additional information
Part of this research was done while this author visited the Hebrew University and was supported by the Leibniz Center
Rights and permissions
About this article
Cite this article
Gonczarowski, J., Warmuth, M.K. Scattered versus context-sensitive rewriting. Acta Informatica 27, 81–95 (1989). https://doi.org/10.1007/BF00263503
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00263503