Notes on Complexity Theory Last updated : October , 2015 Lecture 6
نویسنده
چکیده
As in our previous study of NP, it is useful to identify those problems that capture the essence of PSPACE in that they are the “hardest” problems in that class. We can define a notion of PSPACE-completeness in a manner exactly analogous to NP-completeness: Definition 1 Language L′ is PSPACE-hard if for every L ∈ PSPACE it holds that L ≤p L′. Language L′ is PSPACE-complete if L′ ∈ PSPACE and L′ is PSPACE-hard. Note that if L is PSPACE-complete and L ∈ P, then P = PSPACE. As usual, there is a “standard” (but unnatural) complete problem; in this case, the following language is PSPACE-complete:
منابع مشابه
Notes on Complexity Theory Last updated : October , 2015 Lecture 9 Jonathan Katz 1 The Polynomial Hierarchy
(Note that even though we believe Σi 6= Πi, oracle access to Σi gives the same power as oracle access to Πi. Do you see why?) We show that this leads to an equivalent definition. For this section only, let Σi refer to the definition in terms of oracles. We prove by induction that Σi = Σ O i . (Since Π O i = coΣ O i , this proves it for Πi,Π O i as well.) For i = 1 this is immediate, as Σ1 = NP ...
متن کاملNotes on Complexity Theory Last updated : September 14 , 2011 Lecture 5
We know that there existNP-complete languages. Assuming P 6= NP, any NP-complete language lies in NP \ P. Are there languages that are neither in P nor NP-complete? Ladner’s theorem tells us that there are. As some intuition for Ladner’s theorem, take some language L ∈ NP \ P. Using padding, we will make L “easy enough” so that it can’t be NP-complete, while keeping it “hard enough” so it is no...
متن کاملNotes on Complexity Theory Last updated : December , 2011 Lecture 28
Recall that one motivation for studying non-uniform computation is the hope that it might be easier to prove lower bounds in that setting. (This is somewhat paradoxical, as non-uniform algorithms are more powerful than uniform algorithms; nevertheless, since circuits are more “combinatorial” in nature than uniform algorithms, there may still be justification for such hope.) The ultimate goal he...
متن کاملFriendly Logics , Fall 2015 , Lecture Notes
Since we already know (Theorem 1.3 in lecture notes 3) that the data complexity of FOL model checking is in LOGSPACE, we could use common complexity-theoretic assumptions (such as LOGSPACE 6=NP) to conclude that NP-complete properties of finite graphs such as Hamiltonicity, clique or independent set existence, etc. are not FO-definable. However, we might be interested in asking if properties th...
متن کاملNotes on Complexity Theory Last updated : October , 2005 Handout 8
Recall from last time that a random walk on a graph gave us an RL algorithm for the problem of undirected graph connectivity. In this class, we also saw an RP algorithm for solving 2-SAT (see [2, Chapter 7] for details). We now develop some of the theory behind Markov chains and random walks on (undirected) graphs, toward a proof of the following result that was used to analyze both of the abov...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015