Is Rule 30 Turing complete?

As far as I know, there is no such proof in either direction. A proof of computational universality, like you said, would be to show that rule 30 can simulate computation (Turing machine or equivalent), and it would require extreme patience in experimenting with the cellular automaton as well as some creativity.

Besides, What is the point of Conway Game of Life?

Conway’s initial goal was to define an interesting and unpredictable cell automaton. For example, he wanted some configurations to last for a long time before dying and other configurations to go on forever without allowing cycles.

Keeping this in mind, How do you know if something is Turing-complete? For example, an imperative language is Turing-complete if it has conditional branching (e.g., “if” and “goto” statements, or a “branch if zero” instruction; see one-instruction set computer) and the ability to change an arbitrary amount of memory (e.g., the ability to maintain an arbitrary number of data items).

What is not Turing-complete?

Things that can make a language NOT Turing complete

A Turing machine can make decisions based on what it sees in memory – The ‘language’ that only supports + , – , * , and / on integers is not Turing complete because it can’t make a choice based on its input, but a Turing machine can.

Is the human brain Turing-complete?

You can calculate rule 110 by pen and paper, so at least the brain-pen-paper system is Turing complete. However, the brain is not a Turing machine, probably. … The brain, however, is not a simple universal turing machine in the sense that it doesn’t have a finite set of instructions and an infinite tape-band.

Is Conway Game of Life deterministic?

Conway in the 1970s and is probably, the best known of all cellular automata. Despite very simple rules, the game of life is Turing-complete and deterministic. … The game takes place on a two-dimensional finite or infinite grid whose cells can take two distinct states: “alive” or “dead”.

What is Conway’s Game of Life an example of?

The Game of Life (an example of a cellular automaton ) is played on an infinite two-dimensional rectangular grid of cells. Each cell can be either alive or dead. The status of each cell changes each turn of the game (also called a generation) depending on the statuses of that cell’s 8 neighbors.

What does it mean if a language is Turing-complete?

Practically, what you need to know is that a Turing-complete language (also called a universal language) is one where you can compute anything that any other computational method can compute. In other words, a language that’s non-universal—or Turing incomplete—has some limits on the set of things that it can compute.

How do you prove an instruction set is Turing-complete?

The TLDR version is that two systems can solve the same set of problems if they can run emulators of each other. So one way to prove that a system is Turing complete is to emulate a universal Turing machine. The game of life for example was proven to be Turing complete by emulating a universal Turing machine.

Is minesweeper Turing-complete?

“Infinite Versions of Minesweeper are Turing-complete“.

Is Minecraft Turing complete?

With the formal definition Minecraft is not Turing complete. But neither is your computer or any other real device because you need infinite memory for that. In the more common sense that Turing complete is being used, meaning it is a universal computer then yes, Minecraft is Turing complete.

Is HTML5 Turing complete?

A programming language is Turing complete if it equivalent to a Turing machine. In practice, it means that any algorithm can be implemented. … Apparently, HTML5 + CSS3 is now also Turing complete because it can be used to program a Rule 110 automaton.

Is Power Point Turing complete?

Powerpoint is Turing complete because its animation features can be used to simulate a Turing machine.

Are our brains Turing machines?

According to CCTM, the mind is a computational system similar in important respects to a Turing machine, and core mental processes (e.g., reasoning, decision-making, and problem solving) are computations similar in important respects to computations executed by a Turing machine.

Can a Turing machine simulate a brain?

Thus, Turing machine can’t actually do what brains do, so brains aren’t running algorithms. … We don’t simulate anything with Turing machines, just as we don’t “simulate” things with lambda calculus. We use Turing machines to mathematically determine whether a particular process counts as an algorithm or not.

Is DNA Turing complete?

So no, they can not be Turing-complete. That said, there is quite a number of bio-inspired models of computation that can be studied formally. Sticker systems [1], for instance — an abstraction of recombining DNA fragments — can be shown to reach Turing-power when we assume infinite resources.

Why is Conway’s game of life Undecidable?

Conway’s game of Life can simulate a universal Turing machine which means that it is indeed undecidable by reduction from the halting problem. You can program this Turing machine in the game of Life so that it builds some pattern when it halts that doesn’t occur while it’s still running.

What did John Horton Conway discover?

In geometry, he made key discoveries in the study of symmetries, sphere packings, lattices, polyhedra and tilings, including properties of quasi-periodic tilings as developed by Roger Penrose. In algebra, Conway discovered another important system of numbers, the icosians, with his long-time collaborator Neil Sloane.

Why is the game of life so important?

First popularized in 1970 in the Scientific American (Gardner, 1970), the Game of Life has attracted lasting appeal among both scientific and amateur communities. One reason for its appeal is that it is very simple to program, yet at the same time it appears to exemplify emergent and self-organized behaviour.

Is word Turing-complete?

The answer is yes, but for an unexpected reason. I believe the above comments are correct — given size_t is bounded, you cannot represent a turing machine with unbounded states by using C as intended. However, we can use C in a way which completely circumvents the size_t issue — using only the C preprocessor.

Is JavaScript Turing-complete?

Now if you think about any modern programming language, they also take programs(written by us) as input and run them. Further, any program that can be theoretically written to run for a Turing machine can also be written in JavaScript. Thus, JavaScript is Turing complete. That’s it!

Is C++ Turing-complete?

C++ templates are a Turing-complete language [30] , and thus they allow arbitrary computations on types and constants to be performed at compile time.

Is Turing-complete PDF?

With no recursion and no unbounded loops, PDF is clearly not Turing complete.

What is Alan Turing test?

The Turing Test is a method of inquiry in artificial intelligence (AI) for determining whether or not a computer is capable of thinking like a human being. The test is named after Alan Turing, the founder of the Turing Test and an English computer scientist, cryptanalyst, mathematician and theoretical biologist.

Is SQL a Turing complete language?

SQL as such (i.e. the SQL92 standard) is not turing complete. However, many of the languages derived from SQL, such as Oracle’s PL/SQL and SQL Server’s T-SQL and others are turing complete.