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In computer science, a trace is a set of s … 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 Pierre Cartier and Dominique 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 dependency-homomorphic (see below) 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.eduled processes on one or more computers.
, En mathématiques et en informatique, une t … En mathématiques et en informatique, une trace est un ensemble de mots, où certaines lettres peuvent commuter, et d'autres non. Le monoïde des traces oumonoïde partiellement commutatif libre est le monoïde quotient dumonoïde libre par une relation de commutation de lettres. Le monoïdedes traces est donc une structure qui se situe entre le monoïde libreet le monoïde commutatif libre. L'intérêt mathématique du monoïde des traces a été mis en évidencedans l'ouvrage fondateur . Les traces apparaissent dans la modélisation en programmation concurrente, où les lettres qui peuvent commuter représentent des parties de processus qui peuvent s'exécuter de façon indépendante, alors que les lettres qui ne commutent pas représentent des verrous, leur synchronisation ou l'union de threads. Ce modèle a été proposé dans .de threads. Ce modèle a été proposé dans .
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En mathématiques et en informatique, une t … En mathématiques et en informatique, une trace est un ensemble de mots, où certaines lettres peuvent commuter, et d'autres non. Le monoïde des traces oumonoïde partiellement commutatif libre est le monoïde quotient dumonoïde libre par une relation de commutation de lettres.ar une relation de commutation de lettres.
, In computer science, a trace is a set of s … 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 Pierre Cartier and Dominique 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.s, synchronization points or thread joins.
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Monoïde des traces
, Trace monoid
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