Why can Conway’s Game of Life be classified as a universal machine?

I was recently reading about artificial life and came across the statement, “Conway’s Game of Life demonstrates enough complexity to be classified as a universal machine.” I only had a rough understanding of what a universal machine is, and Wikipedia only brought me as close to understanding as Wikipedia ever does. I wonder if anyone … Read more

Turing machine vs Von Neuman machine

Background The Von-Neumann architecture describes the stored-program computer where instructions and data are stored in memory and the machine works by changing its internal state, i.e an instruction operates on some data and modifies the data. So inherently, there is state maintained in the system. The Turing machine architecture works by manipulating symbols on a … Read more

When have you come upon the halting problem in the field? [closed]

Closed. This question is opinion-based. It is not currently accepting answers. Want to improve this question? Update the question so it can be answered with facts and citations by editing this post. Closed 7 years ago. Improve this question When have you ever personally come upon the halting problem in the field? This can be … Read more

What is Turing Complete?

What does the expression “Turing Complete” mean? Can you give a simple explanation, without going into too many theoretical details? Answer Here’s the briefest explanation: A Turing Complete system means a system in which a program can be written that will find an answer (although with no guarantees regarding runtime or memory). So, if somebody … Read more

What is the difference between the input set of a BSS RAM and a language?

I’m currently learning some things about BSS RAMs. For sake of simplicity, please imagine them as a Turing machine over the reals. Now, this machine gets some real numbers as input. The input values form nearly a string, but are not of finite length as decimal representation. Additionally, there are infinitely many real numbers. A … Read more

Reduce ATM to REGULAR_TM

Consider $\mathsf{REGULAR_{TM}} = \{\langle M \rangle \mid \text{$M$is a TM and$L(M)$is a regular language}\}$. Let $S$ be the following algorithm, which solves $\mathsf{A_{TM}}$: “On input $\langle M, w \rangle$, where $M$ is a TM and $w$ is a string: Construct the following TM $M_2$: $M_2$ = “On input $x$: If $x$ has … Read more

Is the set of context free grammars that generate all words in co-RE?

Is {⟨G⟩|L(G)=∑⋆} in co-RE? ⟨G⟩ is the encoding of a context free grammar. My intuition is that this is false. Answer For A={⟨G⟩∣L(G)≠Σ∗} this procedure, returns “yes” iff there is a word w∉L(G) for a given grammar encoding ⟨G⟩ and never halts otherwise: Assume the input encodes a context-free grammar G. Otherwise, accept the input … Read more

This Universal Turing Machine

I was reading this answer about Turing machines and it refers to a bussiness-card-sized one, which claims to be a universal Turing machine, based on this paper. However, I don’t understand the logic of that particular machine. I understand that in a universal Turing machine the “program” is just another machine encoded in the tape … Read more

Why full Chomsky hierarchy is so detailed, if there are decidable recursive languages?

One can have a look on the Chomsky hierarchy https://en.wikipedia.org/wiki/Chomsky_hierarchy , especially the inset named “Automata theory: formal languages and formal grammars” at the bottom of the page. When one tries to model natural language (e.g. as http://www.grammaticalframework.org/ tries to do it), then one usually aims for the most expressive formal language that is still … Read more

RO turing machine with finite memory

Consider the following: A weak TM is a TM with finite tape in size k which can only read its input values. note: the tape size does not include the input length. I need to determine whether if the weak model is equivalent to a regular TM, or to explain why not and to show … Read more