If the universe is a turing machine, must it be one without an oracle?


Can the universe be simulated by a Turing machine?

All known laws of physics have consequences that are computable by a series of approximations on a digital computer. A hypothesis called digital physics states that this is no accident because the universe itself is computable on a universal Turing machine.

Can a Turing machine only have one state?

At first glance, one-state Turing machines are very weak: the halting problem for them is decidable, and, without memory, they cannot even accept a simple one element language such as L = \{ 1 \} .
The Power of One-State Turing Machines.

Comments: 5 pages, 1 figure
Cite as: arXiv:1901.07125 [cs.FL]
(or arXiv:1901.07125v1 [cs.FL] for this version)

Does a Turing machine need an Accept state?

The accepting and rejecting states must be distinct because the machine cannot simultaneously accept and reject. Therefore, there must be at least two states.

Why Turing machine is universal?

This is the reason the Universal Turing machine was introduced which along with input on the tape takes the description of a machine M. The Universal Turing machine can go on then to simulate M on the rest of the content of the input tape. A Universal Turing machine can thus simulate any other machine.

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What is required for Turing completeness?

In general, for an imperative language to be Turing-complete, it needs: A form of conditional repetition or conditional jump (e.g., while , if + goto ) A way to read and write some form of storage (e.g., variables, tape)

Why is Turing complete important?

Turing completeness, named after Alan Turing, is significant in that every plausible design for a computing device so far advanced can be emulated by a universal Turing machine — an observation that has become known as the Church-Turing thesis.

Can a Turing machine have infinite states?

No. The definition of Turing machines requires that the finite-state control unit have a finite number of states. It’s not allowed to have an infinite number of states.

How many states are required to represent the Turing machine?

A Turing Machine must have at least two states: one that accepts input and one that rejects it. Because the machine cannot accept and reject at the same time, the accepting and rejecting states must be separate. As a result, at least two states are required.

What is a state in a Turing machine?

A state register stores the state of the Turing machine. After reading an input symbol, it is replaced with another symbol, its internal state is changed, and it moves from one cell to the right or left. If the TM reaches the final state, the input string is accepted, otherwise rejected.

How did the Turing machine break enigma?

Cracking the code

This machine was able to use logic to decipher the encrypted messages produced by the Enigma. However, it was human understanding that enabled the real breakthroughs. The Bletchley Park team made educated guesses at certain words the message would contain.

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Are Turing machines real?

Turing’s machine is not a real machine. It’s a mathematical model, a concept, just like state machines, automata or combinational logic. It exists purely in the abstract. (Although “real” implementations of the Turing machine do exist, like in this foundational computer science paper.)

Is Turing machine the first computer?

A Turing machine is the original idealized model of a computer, invented by Alan Turing in 1936. Turing machines are equivalent to modern electronic computers at a certain theoretical level, but differ in many details.

Who really cracked the Enigma code?

Bletchley Park is to celebrate the work of three Polish mathematicians who cracked the German Enigma code in World War II. Marian Rejewski, Henryk Zygalski and Jerzy Różycki will be remembered in a talk on Sunday at the park’s annual Polish Day.

Are humans Turing machines?

A Turing machine is a tuple consisting of an alphabet, a tape, some transition, etc. I am not one of those. So no. A human being is not a Turing machine (or at least, I am not).

Who invented zero?

About 773 AD the mathematician Mohammed ibn-Musa al-Khowarizmi was the first to work on equations that were equal to zero (now known as algebra), though he called it ‘sifr’. By the ninth century the zero was part of the Arabic numeral system in a similar shape to the present day oval we now use.

Who invented laptop?

The First True Laptop Computer
Thai born book and software publisher Adam Osborne (1939–2003) was the founder of Osborne Computer Corp, which produced the Osborne 1 in 1981. It was a portable computer that weighed 24 pounds and cost $1,795.

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