diff --git a/main.typ b/main.typ index cc8cbd5..7960f65 100644 --- a/main.typ +++ b/main.typ @@ -277,6 +277,35 @@ This reduction demonstrates that $halt 2$ is computationally no harder than $halt$, implying that $halt 2$ is at least as undecidable as $halt$. = Daļēja atrisināmība +== Info +A problem is considered partially undecidable if it is not decidable, meaning +there is no algorithm that can correctly determines a "yes" or "no" answer for +every input instance of the problem. +However, it may still be semidecidable, also known as recursively enumerable. + +In the context of Turing machines and computability theory, a problem is +partially undecidable if there exists a Turing machine that halts and produces a +"yes" answer for every instance that belongs to the problem, but may either loop +indefinitely or reject instances that do not belong to the problem. +In other words, there is an algorithm that can recognize the instances that +satisfy the problem's criteria but may not halt on instances that do not. + +A problem being partially undecidable means that there is no total algorithm +that can always produce a correct "no" answer for instances outside the problem. +It may be possible to construct a Turing machine that halts and produces a "no" +answer for certain instances outside the problem, but this is not guaranteed for +all instances. + +#teo( + title: "Raisa teorēma", +)[Ja $F$ nav triviāla (ir $M:F(M)=0$ un $M':F(M')=1$), tad $F$ -- neatrisināma.] + +$A$ -- daļēji atrisināma, ja ir Tjūringa mašīna $T$: +- Ja $A(x)=1$, tad $T(x)=1$. +- Ja $A(x)=0$, tad $T(x)=0$ vai $T(x)$ neapstājas. + +#teo[$A$ -- daļēji atrisināma tad un tikai tad, ja $A$ -- algoritmiski sanumurējama.] + = Algoritmiskā sanumurējamība = TM darbības laiks = NP (neatrisināmas problēmas)