aredepends

Aredepends is a term used in dependency analysis to denote that one item depends on another within a directed graph. It is often written as aredepends(A,B) or expressed with a directed edge A -> B. The concept appears in contexts such as software build systems, package managers, data processing pipelines, and knowledge graphs. The term is not universally standardized and may be described with alternative terminology such as depends-on or requires.

Definition and semantics: Aredepends(A,B) means that the state or availability of A cannot be determined until B has been satisfied. The relation can be direct or transitive; the transitive closure aredepends* captures indirect dependencies. Edges may carry attributes such as version constraints, optional vs mandatory status, or conditional requirements.

Applications and analysis: Aredepends is used to plan execution order, detect potential deadlocks in workflows, and optimize parallelization by identifying independent tasks. In graph algorithms, cycles of aredepends pairs indicate circular dependencies, which are typically resolved by policy (treating the cycle as an error, breaking it, or introducing a fallback mechanism). Representations often use adjacency lists or matrices; common algorithms include topological sort, cycle detection with depth-first search, and Tarjan’s strongly connected components.

Examples: A aredepends B; B aredepends C, implying A aredepends C by transitivity. If A aredepends B and B aredepends A, the pair forms a cycle, requiring cycle handling in any resolver or scheduler.

See also: dependency graph, topological sorting, cycle detection, build systems, package management.