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# Topic: Recursively enumerable

 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. A set A is a recursive set iff both A and the complement of A are recursively enumerable sets. The preimage of a recursively enumerable set under a computable function is a recursively enumerable set. en.wikipedia.org /wiki/Recursively_enumerable_set   (496 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. en.wikipedia.org /wiki/Recursively_enumerable_language   (355 words)

 Recursively enumerable language - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-14) 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)

 Recursively enumerable set - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-14) There is an algorithm that, when given an input — typically an integer or a tuple of integers or a sequence of characters — eventually halts if it is a member of S and otherwise runs forever. In other words the set S is recursively enumerable iff there exists a computable function f with domain(f) = S. Only the complements of recursively enumerable sets can be reliably identified in the limit (Technical report. encyclopedia.worldsearch.com /recursively_enumerable_set.htm   (313 words)

 Definability In The Recursively Enumerable Degrees - Nies, Shore, Slaman (ResearchIndex) 19 The recursively enumerable degrees are dense (context) - Sacks - 1964 13 The undecidability of the recursively enumerable degrees (context) - Harrington, Shelah - 1982 12 An algebraic decomposition of the recursively enumerable deg.. citeseer.ist.psu.edu /213281.html   (691 words)

 Recursively enumerable language - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-14) In mathematics, logic and computer science, a formal language is called recursively enumerable, partially decidable or Turing-recognizable if there exists an algorithm to enumerate all valid strings of the language. A formal language is called recursively enumerable if and only if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language. Note that the set difference L\P and in particular the complement of L need not be recursively enumerable. wikipedia.lotsofinformation.com /wiki/index.php/Recursively_enumerable_language   (247 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). 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. Figure 11.4 in the text adds deterministic context-free languages as a proper subset of context-free languages and recursive languages as a proper subset of recursively enumerable languages. www2.hawaii.edu /~paulac/theory   (1253 words)

 Recursively enumerable language   (Site not responding. Last check: 2007-10-14) Another equivalent definition is that a language L is recursively enumerable if it is empty or if there is an algorithm enumerates the members of the language in following sense: 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. 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: 2007-10-14) The complement of a recursive language is also a recursive language - follows from the fact that we can reverse the "yes" answer to a "no" answer. Recursive languages are also recursively enumerable languages - we can change the halting "no" configurations to configurations with non-halting states. Hence the set of all recursively enumerable languages is infinitely countable. www.simpson.edu /~sinapova/cmsc365/L27-Turing.htm   (805 words)

 Richard A. Shore: Publications The recursively enumerable alpha-degrees are dense, Annals of Mathematical Logic 9 (1976), 123-155. The elementary theory of the recursively enumerable degrees is not aleph The theory of the recursively enumerable weak truth table degrees is undecidable, Journal of Symbolic Logic 57 (1992), 864-874 (with Ambos-Spies and Nies). www.math.cornell.edu /~shore/publications.html   (2374 words)

 Recursively enumerable set   (Site not responding. Last check: 2007-10-14) In the theory of computability (often less suggestively called recursion theory), a set ''S of natural numbers or tuples of natural numbers, or of literal string s, is recursively enumerable or computably enumerable or semi-decidable if it satisfies either (and therefore both) of the following equivalent conditions. The word recursive is in this context taken to be synonymous with computable ; see recursive function. ObjectDumper Recursively dumps all fields of an object, using reflection. www.serebella.com /encyclopedia/article-Recursively_enumerable_set.html   (535 words)

 9. Recursively Enumerable Sets   (Site not responding. Last check: 2007-10-14) Thus, we see that the class of sets generated by partial recursive functions is identical to the class of sets accepted by partial recursive functions. Proposition 9.3 A set is recursive if and only if both it and its complement are recursively enumerable. Since the recursive sets are closed under complementation, it suffices to show that every non-empty recursive set is recursively enumerable. www.cs.pitt.edu /~daley/cs2110/notes/cs2110w_node36.html   (644 words)

 Extension of Embeddings in the Recursively Enumerable Degrees (ResearchIndex) Extension of Embeddings in the Recursively Enumerable Degrees (ResearchIndex) Extension of Embeddings in the Recursively Enumerable Degrees 0.5: The Recursively Enumerable Degrees - Shore (1997) citeseer.ist.psu.edu /248742.html   (383 words)

 91080401.HTM   (Site not responding. Last check: 2007-10-14) If you think about this as a problem in the theory of recursive functions you can see how difficult it would be to come up with a theoretical argument or experimental results that prove this. You are asking is there a recursively enumerable set that includes all the predictions of quantum mechanics (a recursively enumerable set) and all the observed results of experiments (a finite set). Since the union of a finite and recursively enumerable set is a recursively enumerable set the answer is yes. www.ciphersbyritter.com /REALRAND/91080401.HTM   (262 words)

 [No title]   (Site not responding. Last check: 2007-10-14) This proves Recursively enumerable languages are closed under union. A similar picture proves Recursively enumerable languages are closed under intersection. Note that this theorem implies L complement not recursively enumerable => L not recursive Note also that if we exhibit a recursively enumerable L such that L is not recursive, this shows that L complement is not recursively enumerable, and thus recursively enumerable languages are not closed under complementation. ranger.uta.edu /~cook/tcs/l19.html   (304 words)

 CmSc 365 Theory of Computation   (Site not responding. Last check: 2007-10-14) H is a recursively enumerable language - semidecided by the universal Turing machine. Thus we have arrived at a contradiction that follows from the assumption that H is a recursive language. L. L is a reduction of H, H is not recursive, hence L is not a recursive language www.simpson.edu /~sinapova/cmsc365-02/L13-Halt.htm   (822 words)

 An Extension of the Recursively Enumerable Turing Degrees An Extension of the Recursively Enumerable Turing Degrees Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion. Recursively enumerable sets of positive integers and their decision problems. www.math.psu.edu /simpson/papers/extre/extre.html   (1397 words)

 Mathematische Logik und Theoretische Informatik An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees. The theory of the recursively enumerable weak-truth-table degrees is undecidable. Discontinuity of cappings in the recursively enumerable degrees and strongly nonbranching degrees. math.uni-heidelberg.de /logic/ambos/ambospub.html   (1551 words)

 Automated theorem proving - Open Encyclopedia   (Site not responding. Last check: 2007-10-14) For first-order logic it is recursively enumerable, i.e., given unbounded resources, any true theorem can eventually be proven, but invalid theorems cannot always be recognized. For this, it is generally required that each individual proof step can be verified by a primitive recursive function or program, and hence the problem is always decidable. Other techniques would include model checking, which is equivalent to brute-force enumeration of many possible states (although the actual implementation of model checkers requires much cleverness, and does not simply reduce to brute force). open-encyclopedia.com /Automated_theorem_proving   (496 words)

 Learn more about Mathematical logic in the online encyclopedia.   (Site not responding. Last check: 2007-10-14) Essentially, this is Gödel's completeness theorem, although that theorem is usually stated in a way that does not make it obvious that it has anything to do with algorithms. In other words, this set is "recursively enumerable", or, as it is sometimes more suggestively put, "semi-decidable". The set of all universally valid second-order formulas is not even recursively enumerable. www.onlineencyclopedia.org /m/ma/mathematical_logic.html   (543 words)

 PlanetMath: recursively enumerable fulfilling any (and therefore all) of the above conditions is called recursively enumerable. The set of encodings of theorems of Peano arithmetic. Cross-references: sequence, integers, Peano arithmetic, theorems, recursive, one-to-one, onto, recursive function, Turing machine, TFAE, language www.planetmath.org /encyclopedia/RecursivelyEnumerable.html   (108 words)

 91080601.HTM   (Site not responding. Last check: 2007-10-14) -If you think about this as a problem in the theory of recursive functions -you can see how difficult it would be to come up with a theoretical argument -or experimental results that prove this. You are asking is there a recursively -enumerable set that includes all the predictions of quantum mechanics (a -recursively enumerable set) and all the observed results of experiments -(a finite set). Since the union of a finite and recursively enumerable set -is a recursively enumerable set the answer is yes. www.ciphersbyritter.com /REALRAND/91080601.HTM   (231 words)

 Citations: Recursively Enumerable Sets and Degrees - Soare (ResearchIndex)   (Site not responding. Last check: 2007-10-14) ....and there is no recursively enumerable set W such that W M and (lN W) M are both in nite. A countable structure for a computable language is recursive if its domain is recursive and its operations and relations are uniformly recursive. We use the same tree to control the enumeration of A, but assign strategies for the negative requirement N e, as above, to all strings of length 2e 1. citeseer.ist.psu.edu /context/57094/0   (1265 words)

 The Theories of the T, tt and wtt R. E. Degrees: Undecidability and Beyond (ResearchIndex)   (Site not responding. Last check: 2007-10-14) Abstract: We discuss the structure of the recursively enumerable sets under three reducibilities: Turing, truth-table and weak truth-table. 1.1: The Recursively Enumerable Degrees - Shore (1997) 1 The theory of the recursively enumerable weak truth-table de.. citeseer.ist.psu.edu /207009.html   (545 words)

 Chapter 23 Turing Machine Languages We have a theorem that the class of recursively enumerable languages is closed under union. Therefore L is recursively enumerable even though its complement, ALAN, is not. 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)

 Theodore A. Slaman: Bibliography   (Site not responding. Last check: 2007-10-14) Sacks (1966) asked whether the metarecursively enumerable degrees are elementarily equivalent to the recursively enumerable degrees. We show there is a non-recursive recursively enumerable set A such that if W is any low recursively enumerable set, then the join W + A is also low. One recursively enumerable real alpha dominates another one beta if there are nondecreasing recursive sequences of rational numbers (a[n]:n in omega) approximating alpha and (b[n]:n in omega) approximating beta and a positive constant C such that for all n, C(alpha-a[n])>(beta-b[n]). math.berkeley.edu /~slaman/papers/Publications.html   (1927 words)

 Mathematical Preprints by Steffen Lempp   (Site not responding. Last check: 2007-10-14) Abstract: We show that the existential theory of the recursively enumerable degrees in the language L containing predicates for order and n-jump comparability for all n, and constant symbols for least and greatest elements, is decidable. Abstract: We prove that a (recursively) enumerable degree is contiguous iff it is locally distributive. Abstract: A general framework for priority arguments in classical recursion theory, using iterated trees of strategies, is introduced and used to present new proofs of four fundamental theorems of recursion theory. www.math.wisc.edu /~lempp/papers/list.html   (4304 words)

 Recursively enumerable language - Information   (Site not responding. Last check: 2007-10-14) Looking For recursively enumerable language - Find recursively enumerable language and more at Lycos Search. Find recursively enumerable language - Your relevant result is a click away! See the original editable 'Recursively enumerable language' article. www.logicjungle.com /wiki/Recursively_enumerable_language   (396 words)

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