Real-valued affine automata compute beyond Turing machines
Abuzer Yakary{\i}lmaz
TL;DR
This paper demonstrates that affine finite automata with real-valued transitions can recognize uncountably many languages, including some beyond Turing machine capabilities, expanding the understanding of automata computational power.
Contribution
It introduces the use of real-valued transitions in affine automata, showing they can recognize languages beyond Turing computability.
Findings
Affine automata recognize uncountably many languages.
Some recognized languages are non-Turing recognizable.
Real-valued transitions enhance automata computational power.
Abstract
We show that bounded-error affine finite automata recognize uncountably many (and so some non-Turing recognizable) languages when using real-valued transitions.
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · DNA and Biological Computing