2024/08/08 by C. Evans Hedges, Hedges, C. Evans, Ronnie Pavlov +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Materials and Mechanics #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2408.04787
openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are a variety of results in the literature proving forms of computability for topological entropy and pressure on subshifts. In this work, we prove two quite general results, showing that topological pressure is always computable from above given an enumeration for a forbidden list inducing the subshift, and that for strongly irreducible shifts of finite type, topological pressure is computable. Our results apply to subshifts on all finitely generated amenable groups with decidable word problem and generalize several previous results which applied only to ℤd-subshifts. As corollaries, we obtain some results related to ground state energy and entropy, proving that the map sending ϕ to supμ∈ Mσ(X) ∫ ϕdμ is computable/computable from above when PX(ϕ) is, and that the map sending ϕ to its ground state/residual entropy is computable from above when PX(ϕ) is computable. We conclude by giving explicit bounds on computation time of PX(ϕ) in the ℤd setting for SI SFTs and locally constant and rational valued ϕ, and show that in the special case X = Aℤ2, this algorithm runs in singly exponential time.