About: Frantic frog function   Sponge Permalink

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The frantic frog function, denoted \(S(n)\) or \( ext{FF}(n)\), is a cousin of the busy beaver function. \(S(n)\) is defined as the maximum number of state transitions made by an n-state, 2-color Turing machine before halting, given blank input. While first discussed by Tibor Radó, the name "frantic frog" was given by James Harland, as part of his "Zany Zoo" Turing machine research project.

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  • Frantic frog function
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  • The frantic frog function, denoted \(S(n)\) or \( ext{FF}(n)\), is a cousin of the busy beaver function. \(S(n)\) is defined as the maximum number of state transitions made by an n-state, 2-color Turing machine before halting, given blank input. While first discussed by Tibor Radó, the name "frantic frog" was given by James Harland, as part of his "Zany Zoo" Turing machine research project.
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Name
  • Frantic frog function
Author
  • Tibor Radó, named by James Harland
Year
  • 1961(xsd:integer)
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  • >* all computable functions
abstract
  • The frantic frog function, denoted \(S(n)\) or \( ext{FF}(n)\), is a cousin of the busy beaver function. \(S(n)\) is defined as the maximum number of state transitions made by an n-state, 2-color Turing machine before halting, given blank input. While first discussed by Tibor Radó, the name "frantic frog" was given by James Harland, as part of his "Zany Zoo" Turing machine research project. Clearly \(S(n) \geq \Sigma(n)\), since printing \(\Sigma(n)\) ones from a blank tape requires at least \(\Sigma(n)\) steps. Therefore the frantic frog function is uncomputable, and eventually dominates all computable functions.
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