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19 April 2024 |
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One-Way Topological Automata and the Tantalizing Effects of Their Topological Features | | Tomoyuki Yamakami
; | | Date: |
18 Mar 2019 | | Abstract: | We cast new light on the existing models of 1-way deterministic topological
automata by introducing a new, convenient model, in which, as each input symbol
is read, an interior system of an automaton, known as a configuration,
continues to evolve in a topological space by applying continuous transition
operators one by one. The acceptance and rejection of a given input are
determined by observing the interior system after the input is completely
processed. Such automata naturally generalize 1-way finite automata of various
types, including deterministic, probabilistic, quantum, and pushdown automata.
We examine the strengths and weaknesses of the power of this new automata model
when recognizing formal languages. We investigate tantalizing effects of
various topological features of our topological automata by analyzing their
behaviors when different kinds of topological spaces and continuous maps, which
are used respectively as configuration spaces and transition operators, are
provided to the automata. | | Source: | arXiv, 1903.7477 | | Services: | Forum | Review | PDF | Favorites | |
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