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Trace monoid, the Glossary

In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not.^[1]

32 relations: Combinatorics, Commutative property, Computer science, Concatenation, Congruence relation, Dependency graph, Dependency relation, Dominique Foata, Donald Knuth, Formal language, Free monoid, Graph (discrete mathematics), History monoid, Isomorphism, Kleene star, Lecture Notes in Computer Science, Levi's lemma, Lexicographic order, MacMahon's master theorem, Monoid, Natural transformation, Parallel computing, Pierre Cartier (mathematician), Process calculus, Semigroup, String operations, Synchronization (computer science), Thread (computing), Trace cache, Trace theory, Transitive closure, Universal property.
Free algebraic structures
Trace theory

Combinatorics

Combinatorics is an area of mathematics primarily concerned with the counting, selecting and arranging of objects, both as a means and as an end in itself.

See Trace monoid and Combinatorics

Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Computer science

Computer science is the study of computation, information, and automation.

See Trace monoid and Computer science

Concatenation

In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. Trace monoid and concatenation are formal languages.

See Trace monoid and Concatenation

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements.

See Trace monoid and Congruence relation

Dependency graph

In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other.

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Dependency relation

In computer science, in particular in concurrency theory, a dependency relation is a binary relation on a finite domain \Sigma, symmetric, and reflexive; i.e. a finite tolerance relation.

See Trace monoid and Dependency relation

Dominique Foata

Dominique Foata (born October 12, 1934) is a mathematician who works in enumerative combinatorics.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist and mathematician.

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Formal language

In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules called a formal grammar. Trace monoid and formal language are formal languages.

See Trace monoid and Formal language

Free monoid

In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element. Trace monoid and free monoid are formal languages, free algebraic structures and semigroup theory.

See Trace monoid and Free monoid

Graph (discrete mathematics)

In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".

See Trace monoid and Graph (discrete mathematics)

History monoid

In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. Trace monoid and history monoid are formal languages, free algebraic structures and semigroup theory.

See Trace monoid and History monoid

Isomorphism

In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.

See Trace monoid and Isomorphism

Kleene star

In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. Trace monoid and Kleene star are formal languages.

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Lecture Notes in Computer Science

Lecture Notes in Computer Science is a series of computer science books published by Springer Science+Business Media since 1973.

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Levi's lemma

In theoretical computer science and mathematics, especially in the area of combinatorics on words, the Levi lemma states that, for all strings u, v, x and y, if uv.

See Trace monoid and Levi's lemma

Lexicographic order

In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set.

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MacMahon's master theorem

In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra.

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Monoid

In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. Trace monoid and monoid are semigroup theory.

See Trace monoid and Monoid

Natural transformation

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved.

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Parallel computing

Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously.

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Pierre Cartier (mathematician)

Pierre Émile Cartier (born 10 June 1932) is a French mathematician.

See Trace monoid and Pierre Cartier (mathematician)

Process calculus

In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems.

See Trace monoid and Process calculus

Semigroup

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. Trace monoid and semigroup are semigroup theory.

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String operations

In computer science, in the area of formal language theory, frequent use is made of a variety of string functions; however, the notation used is different from that used for computer programming, and some commonly used functions in the theoretical realm are rarely used when programming. Trace monoid and string operations are formal languages.

See Trace monoid and String operations

References

[1] https://en.wikipedia.org/wiki/Trace_monoid

Also known as Free partially commutative monoid, Partially commutative free monoid, Trace language.