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Yuval Filmus
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Levin's universal algorithm is an algorithm such that $t(U,A) < s_V t(V,A) + t_V$. By modifying the algorithm (see for example Hutter's The Fastest and Shortest Algorithm for All Well-Defined Problems), you can make $s_V$ a universal constant, though definitely not $1$ as you require. For related work, consult work by Hirsch, Itsykson and their students, for example this technical report.

Edit: As Squark comments, the runtime of Levin's algorithm also depends on the runtime of $A$, since it has to verify its answers. To get a constant $s_V$, all you need to do is to set the speeds of the various algorithms in geometric progression (rather than arithmetical progression, like in Levin's original algorithm).

Levin's universal algorithm is an algorithm such that $t(U,A) < s_V t(V,A) + t_V$. By modifying the algorithm (see for example Hutter's The Fastest and Shortest Algorithm for All Well-Defined Problems), you can make $s_V$ a universal constant, though definitely not $1$ as you require. For related work, consult work by Hirsch, Itsykson and their students, for example this technical report.

Levin's universal algorithm is an algorithm such that $t(U,A) < s_V t(V,A) + t_V$. By modifying the algorithm (see for example Hutter's The Fastest and Shortest Algorithm for All Well-Defined Problems), you can make $s_V$ a universal constant, though definitely not $1$ as you require. For related work, consult work by Hirsch, Itsykson and their students, for example this technical report.

Edit: As Squark comments, the runtime of Levin's algorithm also depends on the runtime of $A$, since it has to verify its answers. To get a constant $s_V$, all you need to do is to set the speeds of the various algorithms in geometric progression (rather than arithmetical progression, like in Levin's original algorithm).

Source Link
Yuval Filmus
  • 14.5k
  • 1
  • 49
  • 92

Levin's universal algorithm is an algorithm such that $t(U,A) < s_V t(V,A) + t_V$. By modifying the algorithm (see for example Hutter's The Fastest and Shortest Algorithm for All Well-Defined Problems), you can make $s_V$ a universal constant, though definitely not $1$ as you require. For related work, consult work by Hirsch, Itsykson and their students, for example this technical report.