What is required for a language to be Turing-complete?
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)
How can you tell if something is Turing-complete?
Typically, one proves a given language is Turing-complete by providing a recipe for translating any given Turing machine program into an equivalent program in the language in question. Alternately, one can provide a translation scheme from another language, one that has already been proven to be Turing-complete.
Does every Turing machine decide a language?
A TM decides a language if it accepts it and enters into a rejecting state for any input not in the language. A language is recursive if it is decided by a Turing machine. There may be some cases where a TM does not stop. Such TM accepts the language, but it does not decide it.
Is Minecraft Turing-complete?
Since Turing Machines, in a strict sense, require an infinite amount of memory for execution, Minecraft is not Turing complete and neither is your computer or programming languages like Java and C++, which are often deemed as Turing complete.
Can a language be Turing-complete without recursion?
The features used to achieve Turing completeness can be quite different; Fortran systems would use loop constructs or possibly even goto statements to achieve repetition; Haskell and Prolog, lacking looping almost entirely, would use recursion. Even pure functional languages are Turing-complete.
Are all languages Turing-complete?
Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. The concept is named after English mathematician and computer scientist Alan Turing.
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 Turing complete PDF?
With no recursion and no unbounded loops, PDF is clearly not Turing complete.
Can a Turing machine accept multiple languages?
Any particular input to that machine is either always accepted (in the language) or always not accepted (not in the language). So there’s no mechanism by which a single Turing machine even could accept more than one langauge.
Can a Turing machine act as a language recognizer?
Turing machines (TM) Finite state automata can be used to recognize only regular languages.
Are spreadsheets Turing complete?
For example, Excel spreadsheets are Turing complete. That’s not entirely a surprise, since they include a full-fledged programming language for writing macros/extensions. But even without using that, the formula language of Excel can be argued to be Turing complete.
How to prove that a language is Turing complete?
So proving that we can emulate a turing machine is a good way to prove that a language is turing complete, by the way this is not the only way, another way can be to prove that your language is able to describe all the μ -recursive functions.
Is there a Turing equivalent to a computer?
In that sense, real computers are not Turing equivalent, since none of them have an infinite amount of storage.
Why did Alan Turing create the Turing machine?
Alan Turing created a machine that can take a program, run that program, and show some result. But then he had to create different machines for different programs. So he created “Universal Turing Machine” that can take ANY program and run it. Programming languages are similar to those machines (although virtual). They take programs and run them.
What is Turing completeness and why is it important?
From wikipedia: 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.