formaladjacent

Formaladjacent is a term used in discussions of formal language theory and related disciplines to describe a relation between two elements that occur directly next to each other within a specified formal context. It is a label chosen for clarity in analyses of grammars, automata, and derivations, rather than a universally standardized relation.

In a formal grammar, two symbols X and Y are formaladjacent if X immediately precedes Y on the right-hand side of some production, with no symbol between them. For example, in the production A -> B C D, the pairs (B, C) and (C, D) are formaladjacent. The concept can also be extended to the derived string level: two adjacent symbols in a sentential form may be described as formaladjacent when they occur contiguously in that form under the current derivation.

Applications of the notion include parsing and grammar analysis, where identifying formaladjacent pairs helps to reason about locality of dependencies, predict next inputs, or optimize tokenization and error recovery. It can also assist formal verification and model checking by isolating immediate successor relationships in transition systems or derivation steps.

Relation to other ideas is important: formaladjacent is distinct from semantic adjacency (concerned with meaning) and from general adjacency in graphs or trees, since its emphasis is on immediate syntactic succession within a defined formal rule or derivation state. The term is primarily used in niche or pedagogical contexts and is not universally adopted in standard textbooks. See also: adjacency, immediate dominance, parse tree, right-hand side.