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- Trace_monoid abstract "In mathematics and 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 wikiPageRevisionID "606381666".
- Trace_monoid hasPhotoCollection Trace_monoid.
- 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 type Artifact100021939.
- Trace_monoid type FreeAlgebraicStructures.
- Trace_monoid type Object100002684.
- Trace_monoid type PhysicalEntity100001930.
- Trace_monoid type Structure104341686.
- Trace_monoid type Whole100003553.
- Trace_monoid type YagoGeoEntity.
- Trace_monoid type YagoPermanentlyLocatedEntity.
- Trace_monoid comment "In mathematics and 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 "Monoïde des traces".
- Trace_monoid label "Trace monoid".
- Trace_monoid sameAs Monoïde_des_traces.
- Trace_monoid sameAs m.02qnr3g.
- Trace_monoid sameAs Q3321292.
- Trace_monoid sameAs Q3321292.
- Trace_monoid sameAs Trace_monoid.
- Trace_monoid wasDerivedFrom Trace_monoid?oldid=606381666.
- Trace_monoid isPrimaryTopicOf Trace_monoid.