Abstract
Homomorphisms have played an important role throughout the development of language theory. In the last years, new areas of language theory have been developed based on homomorphisms. We survey some recent results in such areas: Starting with the DOL equivalence problem we first mention the notions of homomorphism equivalence and equality sets, and their application to homomorphic representation theorems. We then use lengthpreserving homomorphisms to define grammatical similarity and discuss some striking results from the fast growing area of grammar forms and L forms.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Albert, J., Maurer, H.: The class of context-free languages is not an EOL family; Information Processing Letters 6 (1977), 190–195.
Ainhirn,W., Maurer,H.: On É›-productions in EOL forms; IIG-Technical University of Graz, Manuscript (1978).
Albert,J., Maurer,H., Rozenberg,G.: Simple EOL forms under uniform interpretation generating CF languages; Fundamenta Informatica (to appear).
Culik II,K.: On the decidability of the sequence equivalence problem for DOL systems; Theoretical Computer Science 3 (1977), 75–84.
Culik II,K.: The ultimate equivalence problem for DOL systems; Acta Informatica 10 (1978), 79–84.
Culik II, K.: A purely homomorphic characterization of recursively enumerable sets; Journal of the ACM (to appear).
Culik II,K., Fris, I.: The decidability of the equivalence problem for DOL systems; Information and Control 35 (1977), 20–39.
Cremers, A.B., Ginsburg, S.: Context-free grammar forms; Journal of Computer and Systems Sciences 11 (1975), 86–119.
Culik II,K., Maurer,H.: On simple representations of language families; University of Waterloo Report CS-78-41 (1978).
Culik II,K., Maurer, H.: Propagating chain-free normal forms for EOL systems; Information and Control 36 (1978), 309–319.
Culik II,K., Maurer, H., Ottmann, Th.: On two symbol complete EOL forms; Theoretical Computer Science 6 (1978), 69–92.
Culik II,K., Maurer, H., Ottmann, Th., Ruohonen, K., Salomaa, A.: Isomorphism, form equivalence and sequence equivalence of PDOL forms; Theoretical Computer Science 6 (1978), 143–173.
Culik II,K., Salomaa,A.: On the decidability of homomorphism equivalence for languages; University of Waterloo Report CS-77-26 (1977).
Ehrenfeucht, A., Rozenberg, G.: Elementary homomorphisms and a solution of the DOL sequence equivalence problem; Theoretical Computer Science 7 (1978), 169–183.
Engelfriet,J., Rozenberg,G.: Fixed point languages, equality languages and representations of recursively enumberable languages; FOCS (1978), 123–126.
Ginsburg,S.: A survey of grammar forms — 1977; Manuscript (1977).
Ginsburg,S.: Private communication (1977).
Harrison, M.: Introduction to formal language theory; Addison Wesley, Reading (1978).
Herman, G.I., Rozenberg, G.: Developmental systems and languages; North Holland, Amsterdam (1975).
Karhumäki, J.: The decidability of the equivalence problem for polynomially bounded DOL sequences; RAIRO, Ser. Rouge 11 (1977), 17–28.
Lindenmayer, A.: Mathematical Models for cellular interactions in development; Journal of Theoretical Biology 18 (1968), 280–315.
Maurer,H.: Theoretische Grundlagen der Programmiersprachen — Theorie der Syntax; BI, Mannheim (1969).
Maurer, H., Ottmann, Th., Salomaa, A.: On the form equivalence of L forms; Theoretical Computer Science 4 (1977), 199–225.
Maurer, H., Salomaa, A., Wood, D.: EOL forms; Acta Informatica 8 (1977), 75–96.
Maurer,H., Salomaa,A., Wood,D.: Context-free grammar forms with strict interpretations; IIG-Technical University of Graz, Report 19 (1978).
Maurer,H., Salomaa,A., Wood,D.: Strict context-free grammar forms: completeness and decidability; IIG-Technical University of Graz, Report 20 (1978).
Maurer,H., Salomaa,A., Wood,D.: On generators and generative capacity of EOL forms; IIG-Technical University of Graz, Report 5 (1978).
Maurer, H., Salomaa, A., Wood, D.: Uniform interpretations of L forms; Information and Control 36 (1978), 157–173.
Maurer,H., Salomaa,A., Wood,D.: Synchronized EOL forms under uniform interpretation; McMaster University Report 78-CS-11 (1978).
Maurer, H., Salomaa, A., Wood, D.: On good EOL forms; SIAM Journal on Computing 7 (1978), 158–166.
Maurer,H., Salomaa,A., Wood,D.: Relative goodness of EOL forms; RAIRO, series rouge (to appear).
Nivat, M.: Extensions et restrictions des grammaires algebriques; In: Formal Languages and Programming (ed. R. Aguilar) North Holland, Amsterdam (1976) 83–96.
Nielsen, M.: On the decidability of some equivalence probelems for DOL systems; Information and Control 25 (1974), 166–193.
Rozenberg, G.: L systems, sequences and languages; Lecture Notes in Computer Science 34 (1975), 71–84
Rozenberg, G., Salomaa, A.: The mathematical theory of L systems; In: Advances in Information Systems Sciences (J.Tou, Ed.) 6 (1976), 160–200.
Rozenberg,G., Salomaa,A.: The mathematical theory of L systems; forthcoming.
Salomaa,A.: Formal languages; Academic Press (1973).
Salomaa, A.: DOL equivalence: the problem of iterated morphisms; EATCS Bulletin 4 (1978), 5–12.
Salomaa,A.: Equality sets for homomorphisms of free monoids; Acta Cybernetica (to appear).
Salomaa,A., Soittola,M.: Automata theoretic aspects of formal power series; Springer Verlag (1978).
Wood,D.: Grammar and L forms (in preparation).
Wood, D.: Bibliography of grammatical similarity; EATCS Bulletin 5 (1978), 15–22.
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maurer, H. (1979). New aspects of homomorphisms. In: Weihrauch, K. (eds) Theoretical Computer Science 4th GI Conference. Lecture Notes in Computer Science, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09118-1_2
Download citation
DOI: https://doi.org/10.1007/3-540-09118-1_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09118-9
Online ISBN: 978-3-540-35517-5
eBook Packages: Springer Book Archive