Mike Boyle
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View article: Shift equivalence implies flow equivalence for shifts of finite type
Shift equivalence implies flow equivalence for shifts of finite type Open
Shifts of finite type defined from shift equivalent matrices must be flow equivalent.
View article: Symbolic dynamics and the stable algebra of matrices
Symbolic dynamics and the stable algebra of matrices Open
We give an introduction to the "stable algebra of matrices" as related to certain problems in symbolic dynamics. We consider this stable algebra (especially, shift equivalence and strong shift equivalence) for matrices over general rings a…
View article: Decidability of flow equivalence and isomorphism problems for graph C*-algebras and quiver representations
Decidability of flow equivalence and isomorphism problems for graph C*-algebras and quiver representations Open
We note that the deep results of Grunewald and Segal on algorithmic problems for arithmetic groups imply the decidability of several matrix equivalence problems involving poset-blocked matrices over Z (the integers). Consequently, results …
View article: Security Considerations for Code Signing
Security Considerations for Code Signing Open
A wide range of software products (also known as code)-including firmware, operating systems, mobile applications, and application container images-must be distributed and updated in a secure and automatic way to prevent forgery and tamper…
View article: The mapping class group of a shift of finite type
The mapping class group of a shift of finite type Open
We study the mapping class group of a nontrivial irreducible shift of finite type: the group of flow equivalences of its mapping torus modulo isotopy. This group plays for flow equivalence the role that the automorphism group plays for con…
View article: Recommendation for the entropy sources used for random bit generation
Recommendation for the entropy sources used for random bit generation Open
The Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the Nation's measurement and standards infrastructu…
View article: The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors
The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors Open
Extending work of Hochman, we study the almost-Borel structure, i.e., the nonatomic invariant probability measures, of symbolic systems and surface diffeomorphisms. We first classify Markov shifts and characterize them as strictly universa…
View article: Strong shift equivalence and algebraic K-theory
Strong shift equivalence and algebraic K-theory Open
For a semiring ℛ \mathcal{R} , the relations of shift equivalence over ℛ \mathcal{R} ( SE- ℛ \textup{SE-}\mathcal{R} ) and strong shift equivalence over ℛ \mathcal{R} ( SSE- ℛ \textup{SSE-}\mathcal{R} ) are natural equiva…
View article: BOWEN’S ENTROPY-CONJUGACY CONJECTURE IS TRUE UP TO FINITE INDEX
BOWEN’S ENTROPY-CONJUGACY CONJECTURE IS TRUE UP TO FINITE INDEX Open
For a topological dynamical system (X,f), consisting of a continuous map f: X → X, and a (not necessarily compact) set Z ⊂ X, Bowen [2] defined a dimension-like version of entropy, hX(f,Z). In the same work, he introduced a notion of entro…
View article: Flow equivalence and isotopy for subshifts
Flow equivalence and isotopy for subshifts Open
We study basic properties of flow equivalence on one-dimensional compact\nmetric spaces with a particular emphasis on isotopy in the group of (self-)\nflow equivalences on such a space. In particular, we show that an\norbit-preserving such…