reassociate

Reassociate is a term that denotes forming or forming again a previous association, grouping, or connection. In mathematics and related fields, it is most often used to describe the regrouping of terms in an expression without changing its value, typically through the associativity of the operation involved.

In mathematics, reassociation refers to changing the bracketing of a product or sum, such as moving from (a + (b + c)) to ((a + b) + c). This is valid for exact arithmetic because addition and multiplication are associative. However, in non-associative systems or in computations with finite precision, rearranging terms can affect results due to rounding or numerical instability. Reassociation can be used as a reasoning tool or as a practical step in optimization and evaluation strategies.

In computing and numerical analysis, reassociation transformations are employed by compilers and optimizers to improve parallelism, reduce intermediate values, or enhance numerical stability. By reordering operations that are mathematically equivalent, a program can better utilize hardware resources, though care must be taken with floating-point arithmetic where the order of operations matters for accuracy.

In molecular biology, DNA reassociation, or reannealing, describes the process by which single-stranded DNA bonds reform into double-stranded molecules after denaturation. Cot analysis, which studies reassociation kinetics, helps estimate genome size, repetitive sequence content, and the complexity of genetic material. Environmental conditions such as temperature and salt concentration influence the rate and extent of reassociation.

The term may also be used more generally to describe the act of forming new associations or reestablishing prior connections in social, organizational, or interpersonal contexts.