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Reports (Research Report) Year : 1990

On the regular structure of prefix rewritings


We can consider a pushdown automaton as a word rewriting system with labelled rules applied only in a prefix way. The notion of context-free graph, defined by Muller and Schupp is then extended to the notion of prefix transition graph of a word rewriting system. Prefix transition graphs are context-free graphs, and we show they are also the rooted pattern graphs of finite degree, where a pattern graph produced from a finite graph by iterating the addition of a finite family of finite graphs (the patterns). Furthermore, this characterisation is effective in the following sense : any finite family of patterns generating a graph G having a finite degree and a root, is mapped effectively into a rewriting system R on words such that the prefix transition graph of R is isomorphic to G, and the reverse transformation is effective.


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inria-00075362 , version 1 (24-05-2006)


  • HAL Id : inria-00075362 , version 1


Didier Caucal. On the regular structure of prefix rewritings. [Research Report] RR-1196, INRIA. 1990. ⟨inria-00075362⟩
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