String Compression in FA-presentable Structures.

Dmitry Berdinsky,Sanjay Jain,Bakhadyr Khoussainov,Frank Stephan

Theoretical Computer Science（2023）CCF BSCI 4区

Mahidol Univ | Natl Univ Singapore | Univ Elect Sci & Technol China

Cited 0|Views68

Abstract

We construct a FA–presentation ψ:L→N of the structure (N;S) for which a numerical characteristic r(n) defined as the maximum number ψ(w) for all strings w∈L of length less than or equal to n grows faster than any tower of exponents of a fixed height. This result leads us to a more general notion of a compressibility rate defined for FA–presentations of any FA–presentable structure. We show the existence of FA–presentations for the configuration space of a Turing machine and Cayley graphs of some groups for which it grows faster than any tower of exponents of a fixed height. For FA–presentations of the Presburger arithmetic (N;+) we show that it is bounded from above by a linear function.

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Key words

FA–presentation,FA–presentable structure,Successor function,Presburger arithmetic,Compressibility rate

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