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www.jeremykun.com
We assume the reader is familiar with the concepts of determinism and finite automata, or has read the corresponding primer on this blog. The Mother of All Computers Last time we saw some models for computation, and saw in turn how limited they were. Now, we open Pandrora's hard drive: Definition: A Turing machine is a tuple $ (S, \Gamma, \Sigma, s_0, F, \tau)$, where $ S$ is a set of states, $ \Gamma$ is a set of tape symbols, including a special blank symbol $ b$, $ \Sigma \subset \Gamma$ is a set of input symbols, not including $ b$, $ s_0$ is the initial state, $ A \subset S$ is a set of accepting states, $ R \subset S$ is a set of rejecting states, $ \tau: S - (A \cup R) \times \Gamma \to S \times \Gamma \times \left \{ L, R \right \}$ is a partial func... |
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www.jeremykun.com
Decidability Versus Efficiency In the early days of computing theory, the important questions were primarily about decidability. What sorts of problems are beyond the power of a Turing machine to solve? As we saw in our last primer on Turing machines, the halting problem is such an example: it can never be solved a finite amount of time by a Turing machine. However, more recently (in the past half-century) the focus of computing theory has shifted away from possibility in favor of determining feasibility. |
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www.forwardscattering.org
[AI summary] Nicholas Chapman proves that it is decidable to find the fastest Turing machine for computing functions defined on a finite domain by limiting the search space to machines with a finite number of states based on a reference solution's runtime. |
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emmas.site
A succinct observation on the state of web development |
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