Soundness and Completeness of a algorithm -


i confused soundness , completeness of algorithms.

a sound algorithm never return false result. possible algorithm doesn't return anything?

a complete algorithm address inputs. dose result algorithm return affect completeness of algorithm. example, if sorting algorithm take inputs , return list, doesn't guarantee return sorted list, unsound algorithm, however, complete?

let s set of right answers.

a sound algorithm never includes wrong answer in s, might miss few right answers. => not "complete".

a complete algorithm should every right answer in s: include complete set of right answers. might include few wrong answers. might return wrong answer single input. => not "sound".

so,

a sound algorithm never return false result. possible algorithm doesn't return anything?

it must right. can return nothing.(missed part)

for example, if sorting algorithm take inputs , return list, doesn't guarantee return sorted list, unsound algorithm, however, complete?

well, depends.

if returned lists algorithm forms set s, it's complete because every correct answer included. doesn't mean every single output correct. e.g. s = {b1, b2}. assume that, input a1, correct output b1; input a2, correct output b2. if algorithm returns b2 a1, b1 a2, it's complete not sound.

on other hand, if algorithm returns solution b1 both a1 , a2, it's not complete.

so can't infer whether algorithm complete or not soundness, , vice versa.

refer 7 ways approach soundness , completeness, here.


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