Introduction to Complexity Theory
(Lecture Notes - Corrections and Additions)
Following is a list of major corrections and additions
to the lecture notes.
For more details see
Currently the list contains a single item.
- When defining the class RL Lecture 7 (cf., Sec. 7.6),
one needs to explicitly restrict the machine's running time
(to be polynomial). Failing to do so (i.e., allowing exponential
running time) yields a class that equals NL.
- The class PP as defined in Lecture 7 (cf., Def. 7.6),
is computationally equivalent to the class #P
as defined in Lecture 10 (cf., Def. 10.4)
in the sense that each class is Cook-reducible to the other.
Recall that the class PP was referred to in Lecture 7
as a probabilistic complexity class that allows ``useless''
algorithms (i.e., the difference in their behavior,
on YES and NO-instances, may be negligible).
What we forgot to mention is that PP is strongly related
(as stated above) to the counting (complexity) class #P.
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