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12 votes
4 answers
4k views

reversible Turing machines

Hello, Let T be a Turing machine such that 1) it operates on the alphabet {0,1}, 2) its set of states is A 3) the language it accepts is $L$ . Does there exists a Turing machine S which also ...
Łukasz Grabowski's user avatar
9 votes
4 answers
2k views

Uniqueness in Composition of Polynomials

The following situation came up in my research: Suppose two functions $f$ and $g$ map $[0,\infty)$ to (a subset of) itself. The function $f$ is linear and $g$ is quadratic, but $g$ is one-to-one on ...
Aeryk's user avatar
  • 2,235
13 votes
2 answers
912 views

Is there an analogue of the Lefschetz fixed point theorem for discrete dynamical systems?

Background/Motivation Let $(X, f)$ be a discrete dynamical system. For now, $X$ is just a set and $f$ is just a function $f : X \to X$. Suppose that $f^n$ has a finite number of fixed points for ...
Qiaochu Yuan's user avatar

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