Doperacions

Doperacions is a term used in certain puzzle design and algorithm-education contexts to describe a framework for performing a sequence of operations on an input to reach a target state. It emphasizes transparent stepwise transformation, allowing solvers and learners to inspect how each operation changes the state.

A doperacion is defined by four elements: an initial state, a finite set of primitive operations, a rule for applying operations, and a goal criterion or scoring function. A valid solution consists of a finite sequence of operations that transforms the initial state into a state that satisfies the goal, ideally with minimal cost, length, or complexity.

Common approaches to finding doperacions include greedy methods, backtracking, and constraint-based search, often aided by heuristics for pruning the search space. Doperacions are used in education to teach algorithmic thinking, in game or puzzle design to illustrate problem-solving strategies, and in modeling transformation tasks such as string editing or numeral transformations.

Example: starting from the string "cat", a doperacion might use operations that substitute a character or insert/delete to reach the target "dog" with as few steps as possible. In a numeric variant, starting from 1, allowed operations could be +2 and ×3, seeking 11, which is achieved by 1 + 2 = 3, ×3 = 9, +2 = 11.

See also: transformation systems, sequence planning, puzzle design, algorithm education.