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Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.

1 vote
2 answers
526 views

Is $L=\{\langle M \rangle|M$ makes more than 10 steps on some input$\}$ decidable?

I want to show that it satisfies Rice's theorem: (i) $L$ is non-trivial, since $\langle M\rangle \notin L$ where $L(M)=\emptyset$, as $M$ halts/rejects any input string in the first step. (ii) if $L …
Sid Caroline's user avatar
0 votes
1 answer
378 views

Prove that there exists a machine which decides an infinite subset of halting problem

We already know that $H:=\{\langle M,w\rangle | M$ halts on $w\}$ is undecidable, then how can there possibly be a machine that decides any infinite subset of $H$?
Sid Caroline's user avatar