Entropy conservation for comparison-based algorithms

Comparison-based algorithms are for which the execution of each operation is solely based on outcome a series comparisons between elements [5]. Examples include most sorting algorithms, search and more general such as Heapify constructs heap data structure from an input list computations can be naturally represented via following computational model [12]: (a) structures partially-ordered finite sets; (b) these by topological sorts (aka linear extensions); (c) considering computation states multisets data; (d) represent their induced transformations states. In this view, abstract specification algorithm has state given any possible permutation set (represented, according to (b), discrete together with its all permutations) output sorted again linearly-ordered unique sort). Entropy measure “randomness” or “disorder.” Based we introduce entropy conservation result comparison-based algorithms: “quantitative order gained proportional positional lost.” Intuitively, bears some relation messy office argument advocating chaotic where nothing in right place yet item's known owner, over case item stored owner no longer locate items. Formally, generalise class representable series-parallel partial orders–a well-known computationally tractable [6], [7]. The resulting “denotational” version will extended follow-up work “operational” core part our model.