Abstract
A number of different graph grammar types have been called ”context-free” in the literature. We consider two recent such formalisms, boundary node-label controlled (BNLC) and hyperedge replacement (HR) grammars, from a complexity-theoretical point of view. It is shown that all HR languages, the members of which satisfy a certain separability restriction, are contained in LOGCFL, the class of sets which are log-space reducible to context-free (string) languages. In particular, this implies the existence of efficient sequential as well as parallel recognition algorithms for these languages. Since HR grammars can simulate a large class of BNLC grammars, the same holds for an according class of BNLC languages. Thus, in a sense, a large class of BNLC and HR languages are ”close” to context-free string languages.
We then use these results for investigating the complexity of some graph-theoretical problems restricted to HR languages. It is shown that on HR languages which satisfy the abovementioned constraints, a number of problems (some of which are NP-complete in the general case) have polynomial-time sequential and very fast and feasible parallel solutions.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A.K. Chandra, D.C. Kozen, L.J. Stockmeyer, Alternation. JACM 28 (1981), pp. 114–133.
V.Claus, H.Ehrig, G.Rozenberg (eds.), Graph grammars and their application to Computer Science and Biology. LNCS 73, 1979.
S.A. Cook, Towards a complexity theory of synchronous parallel computation. L'Enseignement mathématique 27 (1981), pp. 99–124.
E.Dahlhaus, M.Karpinski, Parallel complexity for matching restricted to degree defined graph classes. Preprint, Universität Bonn, 1987.
P. Della Vigna, C. Ghézzi, Context-free graph grammars. Information and Control 37 (1978), pp. 207–233.
J. Edmonds, Paths, trees, and flowers. Canad. J. Math. 17 (1965), pp. 449–467.
J.Engelfriet, personal communication, Dec. 1987.
H.Ehrig, M.Nagl, G.Rozenberg (eds.), Graph grammars and their application to Computer Science. LNCS 153, 1983.
J. Feder, Plex languages. Inf. Sci. 3 (1971), pp. 225–241.
M.Garey, D.Johnson, Computers and intractability. Freeman, 1979.
D.Grigoriev, M. Karpinski, The matching problem for bipartite graphs with polynomially bounded permanents is in NC. 28th Proc. IEEE FOCS, 1987.
A. Habel, H.-J. Kreowski, Some structural aspects of hypergraph languages generated by hyperedge replacement. LNCS 247 (1987), pp. 207–219.
A.Habel, H.-J.Kreowski, May we introduce to you: Hyperedge replacement. Proc. 3rd international workshop on graph grammars and their applications to Computer Science, to appear.
J. Hromkovič, Two independent solutions of the 23-years old open problem in one year. EATCS Bulletin 34 (1988), pp. 310–313.
J.E.Hopcroft, J.D. Ullman, Introduction to automata theory, languages, and computation. Addison-Wesley, 1979.
N.Immerman, Nondeterministic space is closed under complement. TR 552, Yale University, July 1987, also in Proc. 3rd Ann. Conf. on Structure in Complexity Theory, 1988.
D. Janssens, G. Rozenberg, Restrictions, extensions, and variations of NLC grammars. Inf. Sci. 20 (1980), pp. 217–244.
H.-J.Kreowski, Rule trees can help to escape hard graph problems. Preprint, Universität Bremen, 1987.
C.Lautemann, Efficient algorithms on graphs represented by decomposition trees. Report No. 6/87, Fachbereich Mathematik/Informatik, Universität Bremen, 1987.
C.Lautemann, Decomposition trees: structured graph representation and efficient algorithms. LNCS 299, pp. 28–39.
T. Lengauer, Efficient algorithms for finding minimum spanning forests of hierarchically defined graphs. LNCS 216 (1986), pp. 153–170.
J.Y.-T. Leung, J. Witthof, O. Vornberger, On some variations of the bandwidth minimization problem. SIAM J. Comp. 13 (1984), pp. 650–667.
T. Pavlidis, Linear and context-free graph grammars. JACM 19 (1972), pp. 11–22.
G. Rozenberg, E. Welzl, Boundary NLC grammars — basic definitions, normal forms and complexity. Information and Control 69 (1986), pp. 136–167.
G. Rozenberg, E. Welzl, Graph-theoretic closure properties of the family of boundary NLC languages. Acta Inf. 23 (1986), pp. 289–309.
G. Rozenberg, E. Welzl, Combinatorial properties of boundary NLC graph languages. Discr. Appl. Math. 16 (1987), pp. 59–73.
W.L. Ruzzo, Tree-size bounded alternation. JCSS 20 (1980), pp. 218–235.
A.O. Slisenko, Context-free graph grammars as a tool for describing polynomial-time subclasses of hard problems. Inf. Proc. Let. 14 (1982), pp. 52–56.
I.H. Sudborough, On the tape complexity of deterministic context-free languages. JACM 25 (1978), pp. 405–414.
R. Szelepcsényi, The method of forcing for nondeterministic automata. EATCS Bulletin 33 (1987), pp. 96–99.
H.Venkateswaran, Properties that characterize LOGCFL. Proc. 19th ACM-STOC (1987), pp. 141–150.
W.Vogler, personal communication, March 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lautemann, C. (1988). Efficient algorithms on context-free graph languages. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_128
Download citation
DOI: https://doi.org/10.1007/3-540-19488-6_128
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19488-0
Online ISBN: 978-3-540-39291-0
eBook Packages: Springer Book Archive