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# Topic: Turing-complete

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###### In the News (Tue 21 May 13)

 NP-complete If one defines the analogue to NP-complete with Turing reductions instead of many-one reductions, the resulting set of problems won't be smaller than NP-complete; it is an open question whether it will be any larger. Note that this diagram is misleading as a description of the mathematical relationship between these problems, as there exists a polynomial-time reduction between any two NP-complete problems; but it indicates where demonstrating this polynomial-time reduction has been easiest. This type of reduction is more refined than the more usual polynomial-time many-one reductions and it allows us to distinguish more classes such as P-complete. www.brainyencyclopedia.com /encyclopedia/n/np/np_complete_1.html

 EECS290n Lecture 17 Notes A Kahn-McQueen network therefore is Turing Complete, the halting problem (the deadlock problem) is not decidable for the whole class. Therefore it can't be the actors and the values, it must be the buffers to fulfill Turing completeness. The question arose, whether a general Dataflow-model is Turing complete. ptolemy.eecs.berkeley.edu /~eal/ee290n/lec18.scribe.html   (509 words)

 Outline.htm Complexity Classes: Relations among complexity measures, time and space-bounded Turing machines, P and NP computations, NP-completeness, P=NP question, definitions and examples of P-complete and NP-complete problems, boundary between class P and NP, examples of P-SPACE complete problems, circuit and PRAM model of computation, efficiently parallelizable languages. Machines with Memory: Finite State Machines, Simulating FSMs with Shallow Circuits, RAM machines, Turing machines, Circuit simulation of a Turing machine. Computability: Techniques of Turing Machine design, recursive functions and Turing machines; functions computed by Turing machines, non-deterministic and alternating Turing machines, time and space complexity of Turing machine computations, halting problem; examples of unsolvable problems about Turing machines. www.cis.umassd.edu /~bmikolajczak/CIS560/Outline.htm   (326 words)

 Turing completeness - Wikipedia, the free encyclopedia Turing completeness is significant in that every plausible design for a computing device so far advanced can be emulated by a universal Turing machine. The computational systems (algebras, calculi) that are discussed as Turing complete systems are those intended for studying theoretical computer science. In computability theory, an abstract machine or programming language is called Turing complete, Turing equivalent, or (computationally) universal if it has a computational power equivalent to a universal Turing machine (a simplified model of a programmable computer). en.wikipedia.org /wiki/Turing_completeness   (900 words)

 BF is Turing-complete By giving a BF program which simulates a particular UTM, we proof that BF is Turing-complete. We can proof that BF is Turing-complete, if we can show for every possible Turing machine, there is an equivalent BF program. A Universal Turing Machine (UTM) is a Turing machine that can simulate some Turing-complete computational model. www.iwriteiam.nl /Ha_bf_Turing.html   (1671 words)

 peano.html While the C preprocessor can be proved not to be Turing complete the C++ compiler can actually perform important work at compile time lightening the load at runtime. With the addition of templates the compiler itself becomes Turing complete. You can make code fragments that are elegantly linked together into complete algorithms at compile time. homepage.mac.com /sigfpe/Computing/peano.html   (778 words)

 Comments on 14482 Ask MetaFilter Oh, and by the way, Postscript and TeX are both turing complete, in case someone wants to use text formatting languages to solve the worlds problems. this is what i was thinking of, and it's not turing completeness, but first class functions. it would be hard to think of a language for which meeting that conditon wasn't equivalent to proving turing completeness. ask.metafilter.com /mefi/14482   (2650 words)

 Degrees of prime models We consider the Turing degrees of prime models of complete decidable theories. In particular we show that every complete decidable atomic theory has a prime model whose elementary diagram is low. If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 www.math.uconn.edu /~solomon/seminar/apr1904.html   (2650 words)

 Turing completeness - Wikipedia, the free encyclopedia In computability theory, an abstract machine or programming language is called Turing-complete, Turing-equivalent, or (computationally) universal if it has a computational power equivalent to a universal Turing machine (a simplified model of a programmable computer). Turing completeness is significant in that every plausible design for a computing device so far advanced can be emulated by a universal Turing machine. One important result from computability theory is that it is impossible in general to determine whether a program written in a Turing-complete language will continue executing forever or will stop within a finite period of time (see halting problem). en.wikipedia.org /wiki/Turing_completeness   (904 words)

 Turing completion without semicolons? - dBforums C could be Turing complete if you can have arbitrary large files. fixed definition and many programming languages are Turing complete. > QED, the Universe is /not/ Turing complete. www.dbforums.com /t706153.html   (1207 words)

 utm.b Daniel B Cristofani (cristofdathevanetdotcom) http://www.hevanet.com/cristofd/brainfuck/ This Turing machine achieves Turing-completeness not by simulating other Turing machines directly, but by simulating a Turing-complete class of tag-systems (a computational model invented by Emil Post and named after the children's game "tag"). Thus, a very direct proof that brainfuck is Turing-complete. The brainfuck cells representing the Turing machine cells are laid out contiguously from the beginning of the tape, except that the head of the Turing machine is represented by a gap of three brainfuck cells, just to the left of the brainfuck cell that represents the current Turing machine cell. www.hevanet.com /cristofd/brainfuck/utm.b   (1487 words)

 Complexity Zoo - Qwiki There exists a problem that is complete for E under polynomial-time Turing reductions but not polynomial-time truth-table reductions [Wat87]. It follows that, if the problems complete for E under Turing reductions do not have measure 1 in E, then BPP does not equal EXP. DistNP has complete problems [Gur87], although unlike for NP this is not immediate. qwiki.caltech.edu /wiki/Complexity_Zoo   (6395 words)

 Brainfuck @ It is also a Turing tarpit, ie a programming language designed to be Turing-complete while minimizing the number of distinct instructions (8 commands in that case, all with 0 operands). A programming language is said to be Turing-complete if it has computational power equivalent to a universal Turing machine. A Turing machine is made of a read/write head going forward or backward along an infinite-length tape divided into cells, a stats register that stores the current state, and an actions table that tells what to do in a defined state, or rather given a state-symbol combination. alx2002.free.fr /esoterism/brainfuck/brainfuck_en.html   (938 words)

 BF is Turing-complete A Universal Turing Machine (UTM) is a Turing machine that can simulate some Turing-complete computational model. We can proof that BF is Turing-complete, if we can show for every possible Turing machine, there is an equivalent BF program. Turing Machine, a very simplistic computing model, which yet is powerfull enough to calculate all possible function which can be calculated. home.wxs.nl /~faase009/Ha_bf_Turing.html   (938 words)

 Citations: DNA models and algorithms for NP-complete problems - Bach, Condon, Glaser, Tanguay (ResearchIndex) In this paper we begin a systematic study of volume bounded molecular computation, and we determine the relations among several models of molecular computation and Turing machine computation. In this paper we begin a systematic study of space bounded molecular computation, and we determine the relations among several models of molecular computation and Turing machine computation. In this case the number of variables which can be used in a formula is bounded by 34 (since 10) The more e#cient heuristic allows us to more than double the number of variables of a formula, and this fact is independent of the current state of technology (see e.g. citeseer.ist.psu.edu /context/62872/0   (3647 words)

 Literature Review: Nature Refutes ID?: The Evolutionary Origin of Complex Features If it is Turing complete then it could have generated in principle the phrase. After reading GP's post, and after some more thought, I agree that the flexibility of the Lenski system (Turing complete) is indeed a strong point, and is not a "red herring". But if Avida is demonstrably a universal Turing machine, then the set of computable algorithms that can be implemented is large -- so large that any specificity claims about the instruction set is rather unbelievable. www.iscid.org /boards/ubb-get_topic-f-18-t-000001-p-17.html   (4075 words)

 Fm - Esolang F2 has been proved Turing-complete without reference to the Turing completeness of other Brainfuck languages, by directly simulating a universal tag system in F2 -- see the external resource below. All Fm languages are therefore Turing-complete, because they can easily simulate F2. It is derived from Brainfuck in the spirit of the Wang program formulation of Turing machines, by using only the five instructions '+' '<' '>' '[' ']' and by applying a cyclic ordering to the alphabet, with '+' changing a letter to the next letter in cyclic order. esoteric.voxelperfect.net /wiki/Fm   (122 words)

 Information and Computation Bibliography This paper investigates the distribution and nonuniform complexity of problems that are complete or weakly complete for ESPACE under nonuniform reductions that are computed by polynomial-size circuits (P/Poly-Turing reductions and P/Poly-many-one reductions). A tight, exponential lower bound on the space-bounded Kolmogorov complexities of weakly P/Poly-Turing-complete problems is established. On isomorphisms and density of NP and other complete sets. theory.lcs.mit.edu /~iandc/References/juedesl1996:13.html   (586 words)

 talk.php?id=16 We describe a classification of CA based on the Turing degrees of their orbits on finite configurations. In this setting, the third Culik-Yu class is \\Sigma_3 complete, whereas the class of of computationally universal CA turns out to be \\Sigma_4 complete. www.ms.mff.cuni.cz /automata/talk.php?id=16   (586 words)

 NP time NP is obviously a superset of P (polynomial time problems solvable by a deterministic Turing Machine in polynomial time) since a deterministic algorithm can be considered as a degenerate form of nondeterministic algorithm. (NP) A set or property of computational decision problems solvable by a nondeterministic Turing Machine in a number of steps that is a polynomial function of the size of the input. If a problem A is in NP and a polynomial time algorithm for A could also be used to solve problem B in polynomial time, then B is also in NP. www.linuxguruz.com /foldoc/foldoc.php?NP+time   (209 words)

 ECCC Report TR01-032 and related Papers In particular, we introduce an hypothesis from which we describe a set in NP that is Turing complete but not truth-table complete. Abstract: We use hypotheses of structural complexity theory to separate various NP-completeness notions. You may contribute to the discussion of this ECCC Report; see the detailed instructions. eccc.hpi-web.de /eccc-reports/2001/TR01-032   (96 words)

 ILovePhilosophy.com Discussion Forums :: View topic - Snow Crash - 'Information Hygiene' Computers are turing complete, but do not possess the idea of the infinite...and cannot by virtue of turing completeness. Look up what it means to be Turing complete and what a simple Turing machine is. Then try and apply that to infinity. The Mill example was not mine, it was Leibnez's and that was before Turing, it was merely meant to highlight my point that the seemingly impossible is in fact highly probable. www.ilovephilosophy.com /phpbb/viewtopic.php?t=139373&start=40   (6132 words)

 final-substitution.html Reference [1pt]: Full credit if a complete and appropriate reference is provided. Quality [6pts]: Full credit if the instructor confirms that you complete the goals discussed with the instructor. If you did not discuss the goals, the instructor will evaluate the quality based on the instructor's expectation based on your topic. www.tcnj.edu /~komagata/cmsc485/03s/exams/final-substitution.html   (853 words)

 08.html Thus, Turing-completeness comes from the semantics of the language and environmental completeness from its pragmatics. Later we show that not every Turing-complete language can have a self-interpreter in this sense. This property forms a distinction between languages: some languages are environmentally complete, while others are not. www.hevanet.com /cristofd/08.html   (4551 words)

 PSPACE Una caracterización alternativa de PSPACE es el grupo de problemas decidibles por una máquina de Turing que se alterna en tiempo polinómico. En teoría de complejidad la clase PSPACE es el grupo problemas de la decisión que se puedan solucionar por una máquina de Turing usando una cantidad polinómica de memoria, y tiempo ilimitado. Los problemas más duros de PSPACE son los problemas de PSPACE-Complete. www.yotor.net /wiki/es/ps/PSPACE.htm   (271 words)

 Scheme Macro Programming And yet, such a macro system is Turing complete: we can write a Turing machine with the restricted R5RS macros. The finite control unit of the Turing machine is a set of simple syntax-rules. As an example, the code implements and tests two particular Turing machines: the addition of natural numbers (in unary) and a decision machine. okmij.org /ftp/Scheme/macros.html#Macro-CPS-programming   (4190 words)

 Comments on 14482 Ask MetaFilter To say that a language is Turing-complete is not to say that it implements these basic functions of some historical computer, but rather that it meets an arbitrary set of requirements that computer scientists call "Turing machines". Simply: a programming language is considered Turing-complete if it can emulate a Turing machine, and a Turing machine can emulate that language. The Church Thesis says that Turing machines can compute anything that can be computed, i.e. ask.metafilter.com /mefi/14482   (2650 words)

 ECCC Report TR00-034 and related Papers Abstract: We consider a class, denoted APP, of real-valued functions f:{0,1}^nrightarrow [0,1] such that f can be approximated, to within any epsilon>0, by a probabilistic Turing machine running in time poly(n,1/epsilon). We argue that APP can be viewed as a generalization of BPP, and show that APP contains a natural complete problem: computing the acceptance probability of a given Boolean circuit; in contrast, no complete problems are known for BPP. ECCC Report TR00-034, accepted on Jun 06, 2000. www.eccc.uni-trier.de /eccc-reports/2000/TR00-034   (155 words)

 strangeGizmo.com : Forth : Re: [colorforth] Eight instruction Turing-complete programming language Previous by thread: [colorforth] Eight instruction Turing-complete programming language Subject: Re: [colorforth] Eight instruction Turing-complete programming language Anyway, pinciples behing BF and Forth languages are a bit different -- first thing that comes to my brain (pardon for tautology) is that Forth allows you define your own words, while in BF you just can use branch/calls. www.strangegizmo.com /forth/ColorForth/msg01390.html   (215 words)

 Universal Turing Machine in XSLT Thus, this stylesheet is a Universal Turing Machine and is an existence proof that XSLT 1.0 is Turing complete. The Turing machine moves its tape head one symbol to the left or to the right, or does not move the tape head, depending on the value of the 'movement' attribute that is returned by the transition function. If the Turing machine moves the tape head to the left of the leftmost symbol, then a blank symbol is inserted at the beginning of the tape and this new blank symbol becomes the current symbol. www.unidex.com /turing/utm.htm   (914 words)

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