Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions

Authors:
Wilfried Huss;Ecaterina Sava;Wolfgang Woess
Affiliations:
-;-;-
Venue:
Theoretical Computer Science
Year:
2010

Citing 3
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An introduction to symbolic dynamics and coding

An introduction to symbolic dynamics and coding
Growth-sensitivity of context-free languages

Theoretical Computer Science - WORDS
Context-free pairs of groups I: Context-free pairs and graphs

European Journal of Combinatorics

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Abstract

A language L over a finite alphabet @S is growth sensitive (or entropy sensitive) if forbidding any finite set of factors F of L yields a sublanguage L^F whose exponential growth rate (entropy) is smaller than that of L. Let (X,E,@?) be an infinite, oriented, edge-labelled graph with label alphabet @S. Considering the graph as an (infinite) automaton, we associate with any pair of vertices x,y@?X the language L"x","y consisting of all words that can be read as labels along some path from x to y. Under suitable general assumptions, we prove that these languages are growth sensitive. This is based on using Markov chains with forbidden transitions.