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  • Programming Language, Turing Completeness and Turing Machine

    - by Amumu
    A programming language is said to be Turing Completeness if it can successfully simulate a universal TM. Let's take functional programming language for example. In functional programming, function has highest priority over anything. You can pass functions around like any primitives or objects. This is called first class function. In functional programming, your function does not produce side effect i.e. output strings onto screen, change the state of variables outside of its scope. Each function has a copy of its own objects if the objects are passed from the outside, and the copied objects are returned once the function finishes its job. Each function written purely in functional style is completely independent to anything outside of it. Thus, the complexity of the overall system is reduced. This is referred as referential transparency. In functional programming, each function can have its local variables kept its values even after the function exits. This is done by the garbage collector. The value can be reused the next time the function is called again. This is called memoization. A function usually should solve only one thing. It should model only one algorithm to answer a problem. Do you think that a function in a functional language with above properties simulate a Turing Machines? Functions (= algorithms = Turing Machines) are able to be passed around as input and returned as output. TM also accepts and simulate other TMs Memoization models the set of states of a Turing Machine. The memorized variables can be used to determine states of a TM (i.e. which lines to execute, what behavior should it take in a give state ...). Also, you can use memoization to simulate your internal tape storage. In language like C/C++, when a function exits, you lose all of its internal data (unless you store it elsewhere outside of its scope). The set of symbols are the set of all strings in a programming language, which is the higher level and human-readable version of machine code (opcode) Start state is the beginning of the function. However, with memoization, start state can be determined by memoization or if you want, switch/if-else statement in imperative programming language. But then, you can't Final accepting state when the function returns a value, or rejects if an exception happens. Thus, the function (= algorithm = TM) is decidable. Otherwise, it's undecidable. I'm not sure about this. What do you think? Is my thinking true on all of this? The reason I bring function in functional programming because I think it's closer to the idea of TM. What experience with other programming languages do you have which make you feel the idea of TM and the ideas of Computer Science in general? Can you specify how you think?

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  • Code Golf: Shortest Turing-complete interpreter.

    - by ilya n.
    I've just tried to create the smallest possible language interpreter. Would you like to join and try? Rules of the game: You should specify a programming language you're interpreting. If it's a language you invented, it should come with a list of commands in the comments. Your code should start with example program and data assigned to your code and data variables. Your code should end with output of your result. It's preferable that there are debug statements at every intermediate step. Your code should be runnable as written. You can assume that data are 0 and 1s (int, string or boolean, your choice) and output is a single bit. The language should be Turing-complete in the sense that for any algorithm written on a standard model, such as Turing machine, Markov chains, or similar of your choice, it's reasonably obvious (or explained) how to write a program that after being executred by your interpreter performs the algorithm. The length of the code is defined as the length of the code after removal of input part, output part, debug statements and non-necessary whitespaces. Please add the resulting code and its length to the post. You can't use functions that make compiler execute code for you, such as eval(), exec() or similar. This is a Community Wiki, meaning neither the question nor answers get the reputation points from votes. But vote anyway!

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  • Are .NET's regular expressions Turing complete?

    - by Robert
    Regular expressions are often pointed to as the classical example of a language that is not Turning complete. For example "regular expressions" is given in as the answer to this SO question looking for languages that are not Turing complete. In my, perhaps somewhat basic, understanding of the notion of Turning completeness, this means that regular expressions cannot be used check for patterns that are "balanced". Balanced meaning have an equal number of opening characters as closing characters. This is because to do this would require you to have some kind of state, to allow you to match the opening and closing characters. However the .NET implementation of regular expressions introduces the notion of a balanced group. This construct is designed to let you backtrack and see if a previous group was matched. This means that a .NET regular expressions: ^(?<p>a)*(?<-p>b)*(?(p)(?!))$ Could match a pattern that: ab aabb aaabbb aaaabbbb ... etc. ... Does this means .NET's regular expressions are Turing complete? Or are there other things that are missing that would be required for the language to be Turing complete?

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  • how useful is Turing completeness? are neural nets turing complete?

    - by Albert
    While reading some papers about the Turing completeness of recurrent neural nets (for example: Turing computability with neural nets, Hava T. Siegelmann and Eduardo D. Sontag, 1991), I got the feeling that the proof which was given there was not really that practical. For example the referenced paper needs a neural network which neuron activity must be of infinity exactness (to reliable represent any rational number). Other proofs need a neural network of infinite size. Clearly, that is not really that practical. But I started to wonder now if it does make sense at all to ask for Turing completeness. By the strict definition, no computer system nowadays is Turing complete because none of them will be able to simulate the infinite tape. Interestingly, programming language specification leaves it most often open if they are turing complete or not. It all boils down to the question if they will always be able to allocate more memory and if the function call stack size is infinite. Most specification don't really specify this. Of course all available implementations are limited here, so all practical implementations of programming languages are not Turing complete. So, what you can say is that all computer systems are just equally powerful as finite state machines and not more. And that brings me to the question: How useful is the term Turing complete at all? And back to neural nets: For any practical implementation of a neural net (including our own brain), they will not be able to represent an infinite number of states, i.e. by the strict definition of Turing completeness, they are not Turing complete. So does the question if neural nets are Turing complete make sense at all? The question if they are as powerful as finite state machines was answered already much earlier (1954 by Minsky, the answer of course: yes) and also seems easier to answer. I.e., at least in theory, that was already the proof that they are as powerful as any computer.

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  • How to work with this turing machine?

    - by Lazer
    This is a screenshot of the applet LogiCell 1.0, link to which I found here. As the bottom left corner shows, this is doing sum 0+1 and the result is 01b (bottom right hand side). I am not able to link what is displayed to what the inputs ans outputs are. For example in this case - seeing the snapshot, how do you determine that the inputs are 0 and 1 and the output is 01?

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  • Turing Machine & Modern Computer

    - by smwikipedia
    I heard a lot that modern computers are based on Turing machine. I'd like to share my understanding and hear your comments. I think the computer is a big general-purpose Turing machine. Each program we write is a small specific-purpose Turing machine. The classical Turing machine do its job based on the input and its current state inside and so do our programs. Let's take a running program (a process) as an example. We know that in the process's address space, there's areas for stack, heap, and code. A classical Turing machine doesn't have the ability to remember many things, so we borrow the concept of stack from the push-down automaton. The heap and stack areas contains the state of our specific-purpose Turing machine (our program). The code area represents the logic of this small Turing machine. And various I/O devices supply input to this Turing machine. The above is my naive understanding about the working paradigm of modern computer. I couln't wait to hear your comments. Thanks very much.

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  • Are non Turing-complete languages considered programming languages at all?

    - by user1598390
    Reading a recent question: Is it actually possible to have a 'useful' programming language that isn't Turing complete?, I've come to wonder if non Turing-complete programming languages are considered programming languages at all. Since Turing-completeness means a language has to have variables to store values as well as control structures ( for, while )... Is a language that lacks these features considered a programming language ?

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  • Is CSS turing complete?

    - by Adam Davis
    CSS isn't, insofar as I know, Turing complete. But my knowledge of CSS is very limited. Is CSS Turing complete? Are any of the existing draft or committees considering language features that might enable Turing completeness if it isn't right now?

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  • Turing machine halting problem

    - by iva123
    Hi, I have a question about turing machines and halting problem. Suppose that we have Atm = {(M,w) where M is a turing machine and w is an input} and HALTtm = {(M,w) where M is a turing machine halts with an input w} I want to prove that HALTtm<=m Atm I've tried some methods but I think they're far from the solution. Anyone can give some clues ??

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  • Turing Model Vs Von Neuman model

    - by Santhosh
    First some background (based on my understanding).. The Von-Neumann architecture describes the stored-program computer where instructions and data are stored in memory and the machine works by changing it's internal state, i.e an instruction operated on some data and modifies the data. So inherently, there is state msintained in the system. The Turing machine architecture works by manipulating symbols on a tape. i.e A tape with infinite number of slots exists, and at any one point in time, the Turing machine is in a particular slot. Based on the symbol read at that slot, the machine change the symbol and move to a different slot. All of this is deterministic. My questions are Is there any relation between these two models (Was the Von Neuman model based on or inspired by the Turing model)? Can we say that Turing model is a superset of Von Newman model? Does functional Programming fit into Turing model. If so how? (I assume FP does not lend itself nicely to the Von Neuman model)

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  • Universal Turing Machine Problems

    - by Pindatjuh
    If I have a machine, call it machine 1, that is able to solve a problem: it's just a machine, not persé a Turing machine. It can solve one specific problem. If this exact same problem can be solved on a Universal Turing Machine, then is my original machine, 1, a Universal Turing Machine too? This does not hold for all problems, which is already ansered. Are there any problems which have this described property at all? If it is absolutely not true, then why? Can someone give an example of a problem to be solved. If this problem is solved by my original machine, 1, definately makes this a Universal Turning Machine? Or does such a problem not exists? If it doesn't exists, why? I'm very interested, but can't figure it out... Thanks. Edit: made the question more clear.

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  • What is the relationship between Turing Machine & Modern Computer ? [closed]

    - by smwikipedia
    I heard a lot that modern computers are based on Turing machine. I just cannot build a bridge between a conceptual Turing Machine and a modern computer. Could someone help me build this bridge? Below is my current understanding. I think the computer is a big general-purpose Turing machine. Each program we write is a small specific-purpose Turing machine. The classical Turing machine do its job based on the input and its current state inside and so do our programs. Let's take a running program (a process) as an example. We know that in the process's address space, there's areas for stack, heap, and code. A classical Turing machine doesn't have the ability to remember many things, so we borrow the concept of stack from the push-down automaton. The heap and stack areas contains the state of our specific-purpose Turing machine (our program). The code area represents the logic of this small Turing machine. And various I/O devices supply input to this Turing machine.

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  • What is the relationship between Turing Machine & Modern Computer ?

    - by smwikipedia
    I heard a lot that modern computers are based on Turing machine. I just cannot build a bridge from a conceptual Turing Machine to a real modern computer. Could someone help me build this bridge? Below is my current understanding. I think the computer is a big general-purpose Turing machine. Each program we write is a small specific-purpose Turing machine. The classical Turing machine do its job based on the input and its current state inside and so do our programs. Let's take a running program (a process) as an example. We know that in the process's address space, there's areas for stack, heap, and code. A classical Turing machine doesn't have the ability to remember many things, so we borrow the concept of stack from the push-down automaton. The heap and stack areas contains the state of our specific-purpose Turing machine (our program). The code area represents the logic of this small Turing machine. And various I/O devices supply input to this Turing machine.

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  • If all programming languages are Turing Complete then why do we have language wars?

    - by kadaj
    There are language wars saying one programming language is better than other.. Consider Lisp and Java; and we can argue that the meta programming capabilities of Lisp is better than that of Java. But that does not mean Java cannot have meta programming capabilities without being another dialect of Lisp. Basically all programming languages are Turing Complete. So doesn't that mean we could solve any solvable problem in all those programming languages?

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  • Practical non-Turing-complete languages?

    - by Kyle Cronin
    Nearly all programming languages used are Turing Complete, and while this affords the language to represent any computable algorithm, it also comes with its own set of problems. Seeing as all the algorithms I write are intended to halt, I would like to be able to represent them in a language that guarantees they will halt. Regular expressions used for matching strings and finite state machines are used when lexing, but I'm wondering if there's a more general, broadly language that's not Turing complete? edit: I should clarify, by 'general purpose' I don't necessarily want to be able to write all halting algorithms in the language (I don't think that such a language would exist) but I suspect that there are common threads in halting proofs that can be generalized to produce a language in which all algorithms are guaranteed to halt. There's also another way to tackle this problem - eliminate the need for theoretically infinite memory. Once you limit the amount of memory the machine is allowed, the number of states the machine is in is finite and countable, and therefore you can determine if the algorithm will halt (by not allowing the machine to move into a state it's been in before).

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  • JFLAP Turing Machine shortcut problem

    - by Robert Lamb
    In JFLAP (http://jflap.org), there are some shortcuts for Turing machine transitions. One of these shortcuts allows you to transition as long as the current tape symbol isn't the indicated symbol. For example, the transition !g,x;R basically says "Take this transition if the current tape symbol is not g". So far, so good. But the transition I want is !?,~;R which basically says "Move right as long as the current symbol is not the end-of-string (empty cell) symbol". The problem is I cannot figure out how to type in "!?". The JFLAP online documentation (http://www.jflap.org/tutorial/turing/one/index.html#syntax) has this to say: The first shortcut is that there exists the option of using the “!” character to convey the meaning of “any character but this character.” For example, concerning the transition (!a; x, R), if the head encounters any character but an “a”, it will replace the character with an “x” and move right. To write the expression “!?”, just type a “1” in when inputting a command. My question is...how do I actually do what that last sentence is trying to explain to me? Thanks for your help! Robert

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  • Turing-Complete language possibilities?

    - by I can't tell you my name.
    In every Turing-Complete language, is it possible to create a working Compiler for itself which first runs on an interpreter written in some other language and then compiles it's own source code? (Bootstrapping) Standards-Compilant C++ compiler which outputs binaries for, e.g.: Windows? Regex Parser and Evaluater? World of Warcraft clone? (Assuming the language gets the necessary API bindings as, for example, OpenGL and the WoW source code is available) (Everything here theoretical) Let's take Brainf*ck as an example language.

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  • A Turing Machine Question

    - by Hellnar
    Greetings, I have been struggling to find a question regarding this theoretical question, even tho it is not directly a programming question, I believe it is really related. Assume a type of Turing machine which cannot have more than 1000 squares. What would be the relationship between the set of such type of recognizable languages and set of normal recognizable languages.

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  • Why is this an invalid Turing machine?

    - by Danny King
    Whilst doing exam revision I am having trouble answering the following question from the book, "An Introduction to the Theory of Computation" by Sipser. Unfortunately there's no solution to this question in the book. Explain why the following is not a legitimate Turing machine. M = { The input is a polynomial p over variables x1, ..., xn Try all possible settings of x1, ..., xn to integer values Evaluate p on all of these settings If any of these settings evaluates to 0, accept; otherwise reject. } This is driving me crazy! I suspect it is because the set of integers is infinite? Does this somehow exceed the alphabet's allowable size? Thanks!

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  • Alan Turing Needs Your Help

    - by Chris Massey
    Well. sort of. Clearly, you are using a computer. If you are on this site, you are probably quite familiar with computers as artifacts of our modern society. Hopefully, you are also familiar with the fact that Alan Turing, logician and mathematician extraordinaire, was instrumental in laying down the foundations of modern computer science, and did a little work to help turn the tide of WWII in the Allies' favor. Hold that thought. A phenomenal collection of Turing's papers (including his first ever...(read more)

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  • Le prix Turing pour un chercheur de légende, Google et Intel applaudissent ce « Nobel de l'informati

    Un chercheur légendaire reçoit le prix Turing Google et Intel applaudissent ce "Nobel de l'informatique" remis à un employé de Microsoft Qui a inventé la métaphore du "bureau" d'un PC ? Qui a introduit le premier la notion d'interface graphique pour le dit bureau ? Qui a créé la première barre des taches ? Qui, en somme, a inventé le "prototype des ordinateurs personnels de réseau" ? Un seul et même homme : Chuck Thacker. Pour tous ses travaux précurseurs qui ont façonné ce que sont les ordinateurs d'aujourd'hui, la ACM (Association for Computing Machinery) vient de lui décerner le prestigieux Prix Turing, équivalent du Prix Nobel dans l...

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  • Project Turing: Beginning RIA Services

        Turing Project Page: [Novice: 9 | Advanced: 6 ]    FAQ | Table of Contents | Definitions What is this and where do I start? Reposted with VB.Net code     From Database to DataGrid The next step in Project Turing is to create a first iteration of the Silverlight application that will retrieve data from our database.  Using our technology of [...]...Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • What are practical guidelines for evaluating a language's "Turing Completeness"?

    - by AShelly
    I've read "what-is-turing-complete" and the wikipedia page, but I'm less interested in a formal proof than in the practical implications of being Turing Complete. What I'm actually trying to decide is if the toy language I've just designed could be used as a general-purpose language. I know I can prove it is if I can write a Turing machine with it. But I don't want to go through that exercise until I'm fairly certain of success. Is there a minimum set of features without which Turing Completeness is impossible? Is there a set of features which virtually guarantees completeness? (My guess is that conditional branching and a readable/writeable memory store will get me most of the way there) EDIT: I think I've gone off on a tangent by saying "Turing Complete". I'm trying to guess with reasonable confidence that a newly invented language with a certain feature set (or alternately, a VM with a certain instruction set) would be able to compute anything worth computing. I know proving you can building a Turing machine with it is one way, but not the only way. What I was hoping for was a set of guidelines like: "if it can do X,Y,and Z, it can probably do anything".

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