Decidability of CPC-irreducibility of subshifts of finite type over free groups
Ban, Jung-Chao; Chang, Chih-Hung; Wu, Yu-Liang (2023-05-30)
Ban, JC., Chang, CH. & Wu, YL. Decidability of CPC-irreducibility of subshifts of finite type over free groups. Semigroup Forum 106, 527–542 (2023). https://doi.org/10.1007/s00233-023-10360-3
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https://urn.fi/URN:NBN:fi-fe2023081797492
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Abstract
This paper attempts to study the irreducibility on complete prefix code (CPC-irreducibility) of a Markov shift over a free group, a topological mixing property first considered for shift spaces over free semigroups that induces chaotic behavior such as the existence of a dense set of periodic points. An example shows that the (d,c)-reduction, an effective algorithm of determination of CPC-irreducibility of Markov shifts over free semigroups (Ban et al. in J Stat Phys 177:1043–1062, 2019), fails for general Markov shifts over free groups. This paper reveals an algorithm for determining the CPC-irreducibility of Markov shifts over both free semigroups and groups. Furthermore, such an examination is finitely checkable, and an upper bound for the complexity of the algorithm is provided.
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