Abstract
We characterize the images of Szilard languages under alphabetical homomorphisms using so called label grammars and show: If L is a label language (i.e. a language generated by such grammar) then L -{λ} is a coding (renaming) of some Szilard language. This result shows that arbitrary homomorphisms do not have more generating power than nonerasing ones except that they generate the empty word. Combining this result with other properties of label languages, established elsewhere, one obtains characterizations of label languages and of codings of Szilard languages including those by finite shuffle expressions and equations.
Since one might interprete label grammars as a special kind of labelled Petri nets, where each transition has exactly one input arc, we solved the elemination problem of λ-transitions for this restricted class of Petri nets, even if there occur infinite firing-sequences using only λ-transitions within a net.
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Literature
M.Höpner, ‘Über den Zusammenhang von Szi lardsprachen und Matrixgrammatiken', Inst. f. Informatik, Univ. Hamburg, Bericht Nr. 12 (1974).
M.Höpner, ‘Eine Charakterisierung der Szi lardsprachen und ihre Verwendung als Steuersprachen', Lect. Notes in Comp. Sc., 26 (1974).
M.Höpner/M.Opp ‘About three equational classes of languages built up by shuffle operations', MFCS 76, Lect. Notes in Comp. Sc., 45 (1976).
M.Höpner/M.Opp ‘Renaming and erasing in Szilard languages', Inst. f. Informatik, Univ. Hamburg, to be published.
M.Penttonen ‘On derivation languages corresponding to context-free grammars', Acta Informatica, 3 (1974).
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© 1977 Springer-Verlag Berlin Heidelberg
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Höpner, M., Opp, M. (1977). Renaming and erasing in szilard languages. In: Salomaa, A., Steinby, M. (eds) Automata, Languages and Programming. ICALP 1977. Lecture Notes in Computer Science, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08342-1_19
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DOI: https://doi.org/10.1007/3-540-08342-1_19
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