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- Trace_monoid abstract "In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order, but allowing certain reshufflings to take place. Traces were introduced by Cartier and Foata in 1969 to give a combinatorial proof of MacMahon's Master theorem. Traces are used in theories of concurrent computation, where commuting letters stand for portions of a job that can execute independently of one another, while non-commuting letters stand for locks, synchronization points or thread joins.The trace monoid or free partially commutative monoid is a monoid of traces. In a nutshell, it is constructed as follows: sets of commuting letters are given by an independency relation. These induce an equivalence relation of equivalent strings; the elements of the equivalence classes are the traces. The equivalence relation then partitions up the free monoid (the set of all strings of finite length) into a set of equivalence classes; the result is still a monoid; it is a quotient monoid and is called the trace monoid. The trace monoid is universal, in that all homomorphic monoids are in fact isomorphic.Trace monoids are commonly used to model concurrent computation, forming the foundation for process calculi. They are the object of study in trace theory. The utility of trace monoids comes from the fact that they are isomorphic to the monoid of dependency graphs; thus allowing algebraic techniques to be applied to graphs, and vice versa. They are also isomorphic to history monoids, which model the history of computation of individual processes in the context of all scheduled processes on one or more computers.".
- Trace_monoid wikiPageExternalLink diekert97partial.html.
- Trace_monoid wikiPageExternalLink cartfoa.html.
- Trace_monoid wikiPageID "10739141".
- Trace_monoid wikiPageLength "10140".
- Trace_monoid wikiPageOutDegree "27".
- Trace_monoid wikiPageRevisionID "686081441".
- Trace_monoid wikiPageWikiLink Category:Combinatorics.
- Trace_monoid wikiPageWikiLink Category:Formal_languages.
- Trace_monoid wikiPageWikiLink Category:Free_algebraic_structures.
- Trace_monoid wikiPageWikiLink Category:Semigroup_theory.
- Trace_monoid wikiPageWikiLink Commutative_property.
- Trace_monoid wikiPageWikiLink Dependency_relation.
- Trace_monoid wikiPageWikiLink Dominique_Foata.
- Trace_monoid wikiPageWikiLink Homomorphism.
- Trace_monoid wikiPageWikiLink Isomorphism.
- Trace_monoid wikiPageWikiLink Kleene_star.
- Trace_monoid wikiPageWikiLink Lecture_Notes_in_Computer_Science.
- Trace_monoid wikiPageWikiLink Levis_lemma.
- Trace_monoid wikiPageWikiLink Lexicography.
- Trace_monoid wikiPageWikiLink MacMahon_Master_theorem.
- Trace_monoid wikiPageWikiLink Monoid.
- Trace_monoid wikiPageWikiLink Natural_transformation.
- Trace_monoid wikiPageWikiLink Parallel_computing.
- Trace_monoid wikiPageWikiLink Pierre_Cartier_(mathematician).
- Trace_monoid wikiPageWikiLink Process_calculus.
- Trace_monoid wikiPageWikiLink Semigroup.
- Trace_monoid wikiPageWikiLink String_operations.
- Trace_monoid wikiPageWikiLink Synchronization_(computer_science).
- Trace_monoid wikiPageWikiLink Thread_(computing).
- Trace_monoid wikiPageWikiLink Transitive_closure.
- Trace_monoid wikiPageWikiLinkText "Trace monoid".
- Trace_monoid wikiPageWikiLinkText "semi-abelian monoid".
- Trace_monoid wikiPageWikiLinkText "trace monoid".
- Trace_monoid wikiPageWikiLinkText "trace".
- Trace_monoid wikiPageWikiLinkText "traces".
- Trace_monoid wikiPageUsesTemplate Template:Citation.
- Trace_monoid wikiPageUsesTemplate Template:Expand_section.
- Trace_monoid wikiPageUsesTemplate Template:Reflist.
- Trace_monoid subject Category:Combinatorics.
- Trace_monoid subject Category:Formal_languages.
- Trace_monoid subject Category:Free_algebraic_structures.
- Trace_monoid subject Category:Semigroup_theory.
- Trace_monoid hypernym Set.
- Trace_monoid type Language.
- Trace_monoid type Combinatoric.
- Trace_monoid type Field.
- Trace_monoid type Language.
- Trace_monoid type Structure.
- Trace_monoid comment "In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order, but allowing certain reshufflings to take place. Traces were introduced by Cartier and Foata in 1969 to give a combinatorial proof of MacMahon's Master theorem.".
- Trace_monoid label "Trace monoid".
- Trace_monoid sameAs Q3321292.
- Trace_monoid sameAs Monoïde_des_traces.
- Trace_monoid sameAs m.02qnr3g.
- Trace_monoid sameAs Q3321292.
- Trace_monoid wasDerivedFrom Trace_monoid?oldid=686081441.
- Trace_monoid isPrimaryTopicOf Trace_monoid.