2002
DOI: 10.1090/s0002-9947-02-03048-9
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Growth and ergodicity of context-free languages

Abstract: Abstract. A language L over a finite alphabet Σ is called growth-sensitive if forbidding any set of subwords F yields a sublanguage L F whose exponential growth rate is smaller than that of L. It is shown that every ergodic unambiguous, nonlinear context-free language is growth-sensitive. "Ergodic" means for a context-free grammar and language that its dependency di-graph is strongly connected. The same result as above holds for the larger class of essentially ergodic context-free languages, and if growth is c… Show more

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Cited by 27 publications
(20 citation statements)
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“…That is, let L G be an automatic structure for G, with some generating set S. Is there a language-theoretic description of the automatic subgroups H ⊂ G such that f L H grows exponentially more slowly than f L G ? This question is closely related to the problem, studied by Ceccherini-Silberstein and Woess [CSW02,CSW03], of deciding what languages are growth sensitive, that is, what languages have the property that prohibiting a set of sub-words reduces the growth rate of the language.…”
Section: Examples and Open Problemsmentioning
confidence: 99%
“…That is, let L G be an automatic structure for G, with some generating set S. Is there a language-theoretic description of the automatic subgroups H ⊂ G such that f L H grows exponentially more slowly than f L G ? This question is closely related to the problem, studied by Ceccherini-Silberstein and Woess [CSW02,CSW03], of deciding what languages are growth sensitive, that is, what languages have the property that prohibiting a set of sub-words reduces the growth rate of the language.…”
Section: Examples and Open Problemsmentioning
confidence: 99%
“…The grammar (and the language it generates) is called ergodic , if is strongly connected. This notion was introduced by Ceccherini and Woess [3] .…”
Section: Grammars Associated With Tree Sets and Their Dependency Di-mentioning
confidence: 99%
“…In the more general context of analytic combinatorics, see the monographs of Flajolet and Sedgewick [12, Section VII.6] and Drmota [9, Section 2.2.5] . For the setting of generating functions associated with grammars, see also [3] . Appealing to [12, Theorem VII.6] , we get the following.…”
Section: Generating Functions Tree Sets and Random Walksmentioning
confidence: 99%
“…quotients of context-free graphs. Group-related examples occur also in Ceccherini-Silberstein and Woess [3] .…”
Section: Introductionmentioning
confidence: 98%