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The vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing an algorithm that solves it; a computational problem is shown to be in P (complexity) by showing an algorithm that solves it in time that is polynomial in the size of the input; etc. However, there are several non-constructive results, where an algorithm is proved to exist without showing the algorithm itself. Several techniques are used to provide such existence proofs.

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  • The vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing an algorithm that solves it; a computational problem is shown to be in P (complexity) by showing an algorithm that solves it in time that is polynomial in the size of the input; etc. However, there are several non-constructive results, where an algorithm is proved to exist without showing the algorithm itself. Several techniques are used to provide such existence proofs. (en)
  • A maioria dos resultados positivos sobre problemas computacionais são provas construtivas, i.e. , um problema computacional é provado pra ser solucionado a partir de um algoritmo que o resolve; um problema computacional mostra-se em P(complexidade) dado que a partir da sua entrada tenha um algoritmo que o resolve em tempo polinomial; etc. No entanto, existem vários resultados não- construtivos, onde a existência de um algoritmo é provada sem mostrar o algoritmo por si só. Várias técnicas são usadas para fornecer a existências dessas provas. (pt)
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  • The vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing an algorithm that solves it; a computational problem is shown to be in P (complexity) by showing an algorithm that solves it in time that is polynomial in the size of the input; etc. However, there are several non-constructive results, where an algorithm is proved to exist without showing the algorithm itself. Several techniques are used to provide such existence proofs. (en)
  • A maioria dos resultados positivos sobre problemas computacionais são provas construtivas, i.e. , um problema computacional é provado pra ser solucionado a partir de um algoritmo que o resolve; um problema computacional mostra-se em P(complexidade) dado que a partir da sua entrada tenha um algoritmo que o resolve em tempo polinomial; etc. No entanto, existem vários resultados não- construtivos, onde a existência de um algoritmo é provada sem mostrar o algoritmo por si só. Várias técnicas são usadas para fornecer a existências dessas provas. (pt)
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  • Non-constructive algorithm existence proofs (en)
  • Existência de Algoritmos com provas Não construtivas (pt)
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