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# Topic: Recursively enumerable language

 Recursively enumerable set - Wikipedia, the free encyclopedia a recursively enumerable language is a recursive enumerable set in the set of all possible words over the alphabet of the language. Matiyasevich's theorem states that every recursively enumerable set is a Diophantine set (the converse is trivially true). The preimage of a recursively enumerable set under a computable function is a recursively enumerable set. en.wikipedia.org /wiki/Recursively_enumerable   (625 words)

 Recursively enumerable language - Wikipedia, the free encyclopedia A recursively enumerable formal language is a recursively enumerable subset in the set of all possible words over the alphabet of the language. A recursively enumerable language is a formal language for which there exists a Turing machine (or other computable function) which will enumerate all valid strings of the language. A recursively enumerable language is a formal language for which there exists a Turing machine (or other computable function) that will halt and accept when presented with any string in the language as input but may either halt and reject or loop forever when presented with a string not in the language. en.wikipedia.org /wiki/Recursively_enumerable_language   (382 words)

 Recursively enumerable language - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-08) This is merely a special case of the concept of a recursively enumerable set. Note that, if L is infinite, the enumerating algorithm provided by definition 2 can be chosen so that it avoids repetitions, since we can test whether the string produced for number n is "already" produced for a number which is less than n. In general, if a language L is not recursive, then the language consisting of all strings together with a marker symbol saying whether it is or is not in L is not recursively enumerable. www.encyclopedia-online.info /Recursively_enumerable_language   (776 words)

 [No title]   (Site not responding. Last check: 2007-10-08) These languages are also known as the recursively enumerable language">recursively enumerable languages. A recursively enumerable language in mathematics, logic and computer science, is a type of language">formal language which is also called recursively enumerable, partially decidable or Turing-recognizable. # A recursively enumerable language is a formal language for which there exists a Turing machine (or other computable function) that will halt and accept when presented with any string in the language as input. www.worldhistory.com /wiki/R/Recursively-enumerable-language.htm   (341 words)

 [No title]   (Site not responding. Last check: 2007-10-08) (d) The complement of a recursively enumerable language is a recursively enumerable language. (g) A CFL is a recursively enumerable language (h) The intersection of a CFL and a recursively enumerable language is recursive (i) The intersection of a CFL and a recursive language is recursive (j) My answers to (f) through (i) are all correct. Question 5 Give a grammar in CNF for the language consisting of all strings of a's and b's where the number of a's is not equal to the number of b's. www.engr.uvic.ca /~csunion/exams/CSC320_K92_Final.txt   (406 words)

 A Hierarchy of Formal Languages and Automata A language is recursive on a given alphabet if there’s a Turing machine that accepts the language and halts on every string in the alphabet (but not the empty string, remember). Since we have an algorithm to determine what language the word is in, the language is recursive as well as recursively enumerable. Theorem 11.5 establishes that the family of recursive languages is a proper subset of the family of recursively enumerable languages, not a surprising fact given the previous theorems. www2.hawaii.edu /~paulac/theory   (1253 words)

 Recursively enumerable language   (Site not responding. Last check: 2007-10-08) Note that if L is infinite the enumerating algorithm provided by definition can be chosen so that it avoids since we can test whether the string for number n is "already" produced for a number is less than n. Some partially decidable languages have an algorithm always halts and answers YES or NO Those languages are called decidable languages or recursive languages. In general if a language L is not recursive then the language of all strings together with a marker saying whether it is or is not L is not recursively enumerable. www.freeglossary.com /Recursively_enumerable_language   (814 words)

 CmSc 365 Theory of Computation   (Site not responding. Last check: 2007-10-08) A language is generated by a unrestricted grammar if and only if it is recursively enumerable. Recursive languages are also recursively enumerable languages - we can change the halting "no" configurations to configurations with non-halting states. The complement of a recursively enumerable language is not recursively enumerable - storm.simpson.edu /~sinapova/cmsc365-02/L11-TuringRandom.htm   (631 words)

 CMPSCI 601 Solutions to Midterm Exam, Summer 2003 language reduces to A. We need a reduction f such that for any number n, f(n) is in A iff n is in K. Note the type of f(n) carefully, as it should be a triple (M,w,x) where M is a machine and w and x are strings. This language is recursive (in fact it is even in P) and recursive languages cannot be r.e.-complete. To see that it is recursive we need to show an algorithm that inputs G and w and determines whether w is in L(G). www.cs.umass.edu /~barring/cs601sum03/exam/midsol.html   (970 words)

 Recursively enumerable language   (Site not responding. Last check: 2007-10-08) Note that, if L is infinite, the enumerating algorithm provided bydefinition 2 can be chosen so that it avoids repetitions, since we can test whether the string produced for number n is"already" produced for a number which is less than n. Those languages arecalled decidable languages or recursive languages.Some problems are recursively enumerable but not recursive. In general, if a language L is not recursive, then the language consisting of all strings together with a marker symbolsaying whether it is or is not in L is not recursively enumerable. www.therfcc.org /recursively-enumerable-language-45959.html   (732 words)

 [No title] The concept of networks of language processors is introduced as a framework for modelling parallel and distributed computations on multisets of strings (string collections with possibly more than one occurrences of the same string), see also [10], [11]. Each RE language is the morphic image of the intersection with a regular language of a language generated by such a system. It is shown, that any recursively enumerable language can be generated by a non-centralized returning PC grammar system with three context-sensitive components (two is not enough'' will be shown in [39]). www.sztaki.hu /mms/pcbib.html   (9095 words)

 Viliam Geffert - Abstracts Abstract: A new representation for recursively enumerable languages is presented. Abstract: The paper investigates the properties of the class of languages that are generated by phrase-structure grammars having all of the rules context-free, with the exception of a single rule, which is of the form $AB\rightarrow\varepsilon$. The importance of this language class follows from the fact that using just two non-context-free rules, or using a single non-context-free rule with a left hand side of length three, gives grammars capable of generating any recursively enumerable language. kosice.upjs.sk /~kmi/Geffert/Gefww3.htm   (1374 words)

 CSC 4170 Recursively Enumerable But Not Recursive   (Site not responding. Last check: 2007-10-08) We have now defined a recursively enumerable language L and shown by contradiction that -L is not recursively enumerable. But -L is not recursively enumerable; therefore L must not be recursive. We have therefore shown that L is recursively enumerable but not recursive, therefore the set of recursive languages is a proper subset of the set of recursively enumerable languages. www.seas.upenn.edu /~cit596/notes/dave/relang10.html   (229 words)

 CmSc 365 Theory of Computation The class of recursive languages is closed under complement. Thus there is a class of languages, such that given a string we can tell whether it is in the language or not - these are the recursive languages. The class of recursively enumerable languages is closed under complement. www.simpson.edu /~sinapova/cmsc365-02/L10-Turing.htm   (579 words)

 Recursively enumerable language Language Center in Hamburg, Germany, is a large institute which offers language classes in German as a foreign language as well as classes in 18 other languages plus language travels in 20 different countries. The Language Dorm is a selective house whose objective is to create a community of foreign language students and native speakers to foster the learning and sharing of culture and language. Language combining C and Linda, gives six functions for concurrent process coordination, can be added to any other sequential language, unlike many other parallel languages, programmers needn't learn a new language. www.omniknow.com /common/wiki.php?in=en&term=Recursively_enumerable_language   (1878 words)

 Chapter 23 Turing Machine Languages If a language is recursive, then there is a Turing machine for it that does not have a loop set. We have a theorem that the class of recursively enumerable languages is closed under union. The membership question for the recursively enumerable languages is known as the halting problem, since halting means accepting on a Turing machine. www.mathsci.appstate.edu /~dap/classes/2490/chap23.html   (2434 words)

 Leiden TCS - DNA Computing, an ongoing workshop We prove how any recursively enumerable language can be represented as the projection of the intersection of two morphic images of a specific language L, e.g., L can be chosen as the copy language or the reversed copy language for some alphabet V. Moreover, we point out how these results arise from bidirectional sticker systems. We propose to "compute by carving" by using as sequences of languages to be removed "regular sequences of languages": start with a regular language and iteratively apply to it a sequential transducer (a gsm). Here again formal languages are useful -- there is a close relation of the sets of DNA molecules produced by self-assembly to the Chomsky Hierarchy of languages: linear DNA produces regular languages, branched DNA produces context-free languages, and 2D sheets of DNA produce recursivelly enumerable languages. www.liacs.nl /CS/TCS/ongoing/abstracts.html   (3357 words)

 FinalSpring98 T F (c) The union of a context free language and a regular language must be recursive. L2 and L2 is a regular language, then L1 must be a regular language. T F (o) The complement of a recursively enumerable language must not be recursive. www.cs.utexas.edu /users/ear/cs341/FinalSpring98.html   (642 words)

 Recursively enumerable language A recursively enumerable formal language is a recursively enumerable subset in the set of all possible... a recursively enumerable language is a recursive enumerable set in the set of all... Definition of recursively Enumerable Language A language that is recognized (by halting in an accepting state) but may have strings "rejected" by not terminating. www.logicjungle.com /wiki/Recursively_enumerable_language   (330 words)

 Quals: Computer Theory and Algorithms - SEWiki A recursively language is the set of strings accepted by some Turing machine that halts on all input. A recursively enumerable language is the set of strings accepted by some Turing machine that halts on "yes" instances. A trivial property is one that all of the languages lack or all have. www.cs.wm.edu /~coppit/wiki/index.php?title=Quals:_Computer_Theory_and_Algorithms   (6730 words)

 [No title] If the complement of a recursively enumerable language L is context free, then L must be recursive. The intersection of a context free language and a recursively enumerable language could be regular. Given a language L, if there exists a TM that decides L, then it is possible that L is context free. www.cs.utexas.edu /~cline/ear/Slides/Turing/TuringSlidesReview.doc   (476 words)

 Test outline:   (Site not responding. Last check: 2007-10-08) _F__18.The complement of a recursively enumerable language is recursively enumerable. If a language is decidable, it is recursively enumerable. N is decidable and every language is a subset of N. __T If every proper subset of a set is decidable, the set is decidable. www.runet.edu /~jhelm/classes/revfinal.htm   (354 words)

 CSC 4170 Non-Recursively Enumerable Languages   (Site not responding. Last check: 2007-10-08) Since recursively enumerable languages are those whose strings are accepted by a Turing machine, the set of recursively enumerable languages is also enumerable. Therefore, there must be languages that are not computable by a Turing machine. Using the enumerations described earlier, let string i belong to language X if and only if it does not belong to language i. www.seas.upenn.edu /~cit596/notes/dave/relang8.html   (131 words)

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