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- Word_problem_(mathematics) abstract "In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities E, and two expressions x and y, is it possible to transform x into y using the identities in E as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable.Many, if not most all, undecidable problems in mathematics can be posed as word problems; see the list of undecidable problems for many examples.".
- Word_problem_(mathematics) wikiPageID "3852079".
- Word_problem_(mathematics) wikiPageLength "10214".
- Word_problem_(mathematics) wikiPageOutDegree "49".
- Word_problem_(mathematics) wikiPageRevisionID "701673110".
- Word_problem_(mathematics) wikiPageWikiLink Abelian_group.
- Word_problem_(mathematics) wikiPageWikiLink Abstract_algebra.
- Word_problem_(mathematics) wikiPageWikiLink Abstract_rewriting_system.
- Word_problem_(mathematics) wikiPageWikiLink Algebra.
- Word_problem_(mathematics) wikiPageWikiLink Category:Abstract_algebra.
- Word_problem_(mathematics) wikiPageWikiLink Category:Combinatorics_on_words.
- Word_problem_(mathematics) wikiPageWikiLink Category:Computational_problems.
- Word_problem_(mathematics) wikiPageWikiLink Category:Rewriting_systems.
- Word_problem_(mathematics) wikiPageWikiLink Combinatory_logic.
- Word_problem_(mathematics) wikiPageWikiLink Complete_Heyting_algebra.
- Word_problem_(mathematics) wikiPageWikiLink Computer_science.
- Word_problem_(mathematics) wikiPageWikiLink Confluence_(abstract_rewriting).
- Word_problem_(mathematics) wikiPageWikiLink Decidability_(logic).
- Word_problem_(mathematics) wikiPageWikiLink Decision_problem.
- Word_problem_(mathematics) wikiPageWikiLink Finitary.
- Word_problem_(mathematics) wikiPageWikiLink Free_lattice.
- Word_problem_(mathematics) wikiPageWikiLink Generator_(mathematics).
- Word_problem_(mathematics) wikiPageWikiLink Ground_expression.
- Word_problem_(mathematics) wikiPageWikiLink Group_(mathematics).
- Word_problem_(mathematics) wikiPageWikiLink Heyting_algebra.
- Word_problem_(mathematics) wikiPageWikiLink Integer.
- Word_problem_(mathematics) wikiPageWikiLink Join_and_meet.
- Word_problem_(mathematics) wikiPageWikiLink Knuth–Bendix_completion_algorithm.
- Word_problem_(mathematics) wikiPageWikiLink Lambda_calculus.
- Word_problem_(mathematics) wikiPageWikiLink Lattice_(order).
- Word_problem_(mathematics) wikiPageWikiLink List_of_mathematical_jargon.
- Word_problem_(mathematics) wikiPageWikiLink List_of_undecidable_problems.
- Word_problem_(mathematics) wikiPageWikiLink Mathematics.
- Word_problem_(mathematics) wikiPageWikiLink Munn_tree.
- Word_problem_(mathematics) wikiPageWikiLink Normal_form_(abstract_rewriting).
- Word_problem_(mathematics) wikiPageWikiLink Partially_ordered_set.
- Word_problem_(mathematics) wikiPageWikiLink Presentation_of_a_group.
- Word_problem_(mathematics) wikiPageWikiLink Rewriting.
- Word_problem_(mathematics) wikiPageWikiLink Semigroup.
- Word_problem_(mathematics) wikiPageWikiLink Substitution_(logic).
- Word_problem_(mathematics) wikiPageWikiLink Term_(logic).
- Word_problem_(mathematics) wikiPageWikiLink Turing_machine.
- Word_problem_(mathematics) wikiPageWikiLink Undecidable_problem.
- Word_problem_(mathematics) wikiPageWikiLink Unification_(computer_science).
- Word_problem_(mathematics) wikiPageWikiLink Universal_algebra.
- Word_problem_(mathematics) wikiPageWikiLink Word_problem_for_groups.
- Word_problem_(mathematics) wikiPageWikiLinkText "Word problem (mathematics)".
- Word_problem_(mathematics) wikiPageWikiLinkText "check".
- Word_problem_(mathematics) wikiPageWikiLinkText "word problem (mathematics)".
- Word_problem_(mathematics) wikiPageWikiLinkText "word problem for the presentation of an algebraic structure".
- Word_problem_(mathematics) wikiPageWikiLinkText "word problem".
- Word_problem_(mathematics) wikiPageWikiLinkText "word problems".
- Word_problem_(mathematics) wikiPageWikiLinkText "words".
- Word_problem_(mathematics) date "July 2013".
- Word_problem_(mathematics) date "June 2013".
- Word_problem_(mathematics) reason "In which algebra? It is certainly decidable in ℤ".
- Word_problem_(mathematics) reason "In which lattice precisely? Unification maps two terms to a substitution, while term lattice meet maps two terms to a term, and substitution lattice meet maps two substitutions to a substitution.".
- Word_problem_(mathematics) reason "The solution of a word problem was explained above to be an algorithm, not a set.".
- Word_problem_(mathematics) wikiPageUsesTemplate Template:!.
- Word_problem_(mathematics) wikiPageUsesTemplate Template:About.
- Word_problem_(mathematics) wikiPageUsesTemplate Template:Clarify.
- Word_problem_(mathematics) wikiPageUsesTemplate Template:Clear.
- Word_problem_(mathematics) wikiPageUsesTemplate Template:Main.
- Word_problem_(mathematics) wikiPageUsesTemplate Template:Reflist.
- Word_problem_(mathematics) wikiPageUsesTemplate Template:Technical.
- Word_problem_(mathematics) subject Category:Abstract_algebra.
- Word_problem_(mathematics) subject Category:Combinatorics_on_words.
- Word_problem_(mathematics) subject Category:Computational_problems.
- Word_problem_(mathematics) subject Category:Rewriting_systems.
- Word_problem_(mathematics) hypernym Problem.
- Word_problem_(mathematics) type Disease.
- Word_problem_(mathematics) type Combinatoric.
- Word_problem_(mathematics) comment "In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set.".
- Word_problem_(mathematics) label "Word problem (mathematics)".
- Word_problem_(mathematics) sameAs Q3406273.
- Word_problem_(mathematics) sameAs Problème_du_mot.
- Word_problem_(mathematics) sameAs m.0b3b2f.
- Word_problem_(mathematics) sameAs Q3406273.
- Word_problem_(mathematics) wasDerivedFrom Word_problem_(mathematics)?oldid=701673110.
- Word_problem_(mathematics) isPrimaryTopicOf Word_problem_(mathematics).