In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity class was defined by Gill in 1977.

Pp (Complexity) Lecture Notes and Tutorials PDF

### PP Attachment and Argumenthood

6 (10a) is of course ambiguous between NP or VP attachment of the PP; I am concen- trating on ... A very similar test is proposed by Grimshaw (1990), who notes.by CT Schütze · Cited by 121 · Related articles

### Circuit Complexity and Computational Complexity

Circuit Complexity & Computational Complexity. Lecture Date: 7 January 1991 ... Handbook of Theoretical Computer Science. ∗. CSE Theory Lab. QA76.H279 ...by S Buss · 1992 · Related articles

### Kolmogorov Complexity and Computational Complexity

by L Fortnow · Cited by 12 — Of course this definition of Kolmogorov complexity makes any complexity theorist cringe: what good is a small ... Unique-SAT is easy implies NP = RP [VV86] and P = UP. ... volume 2751 of Lecture Notes in Computer Science, pages 303–310.

### The Complexity of Complexity

Nov 14, 2016 — Indeed, since complexity theory almost always resorts to reducibility in ... much less than |x|), the technical description of what it means for U(d) = x is ... RP ⊆ BPP), and the exponential-time analogs of P and NP (EXP and ...by E Allender · 2016 · Cited by 16 · Related articles

### Space complexity 1 Space complexity

Space complexity. Notes by Jonathan Katz, lightly edited by Dov Gordon ... will also consider the space complexity of non-deterministic turing machines. In direct ...

### The Complexity of intersectionality

The association of the anticategorical approach with the kind of complexity introduced by studies of intersectionality may have also resulted from the tendency to ...by L McCall · 2005 · Cited by 7076 · Related articles

### The Complexity Zoo

by S Aaronson · Cited by 127 — In descriptive complexity, uniform AC0 can be characterized as the class of problems expressible by ... Note that this is not the same as the BPP version of AvP. ... If BPP contains NP, then RP = NP [Ko82] and PH is contained in BPP [Zac88].

### 9 Approximation and Complexity

An approximation algorithm for an optimization problem is ... An optimization problem has a polynomial time approximation scheme (or PTAS) if ... For example,.

### Algorithms and Complexity

Mar 2, 2012 — So in the problem of this example, testing the primality of a given integer n, the length of the ... trivial case, very specific instructions as to how to deal with this graph. ... This is true of the Adleman, Pomerance, Rumely test also.

### Algorithms and Complexity

Apr 1, 2017 — We will now look at the computational complexity of this algorithm. ... to discuss the rates of growth of different functions and to introduce the five.by HS Wilf · 1994 · Cited by 98 · Related articles

### Computability and Complexity

by J Kleinberg · Cited by 4 · Related articlesto a fully general model of computation requires some further fundamental ideas, ... Cryptography has been revolutionized by the theory of complexity, for the.

### 15.083 Lecture 2: Complexity

Complexity. • The classes P and NP. • The classes NP-complete and NP-hard. • What if a problem is NP hard? 2 Efficient algorithms. Slide 2. • The LO problem.

### 2.1 Complexity Classes

Sep 15, 2004 — Note that while RP is a class of languages, we may call an algorithm A an “RP algorithm” if it satisfies the conditions in the above definition.

### Algorithms and Complexity

Mar 2, 2012 — This book is about algorithms and complexity, and so it is about ... Now let's introduce a hierarchy of functions according to their rates of growth ...by HS Wilf · 1994 · Cited by 98 · Related articles

### recursion and complexity

Recursion and complexity, Version 2.0, April 26, 2015, 19:42. ii. Page 5. PREFACE. This is the present state of a developing set of lecture notes that I have.by YN MOSCHOVAKIS · Cited by 7 · Related articles

### Complexity of Problems

This led to the development of computational complexity theory ... taken by the computation T(x). (Note that if T(x) does not halt, then is undefined.) T. Time. )(.

### 32 Summary of Complexity Theory

Definition (Space Complexity of a Nondeterministic TM) ... Providing a polynomial algorithm to SAT solves the P versus NP dilemma. 5 / 12 ... Note that the.

### sorting and asymptotic complexity

Quintessential divide-and-conquer algorithm ... Good sorting algorithms that do not use so much ... Use InsertionSort (for example) for sets of size, say, ≤ 9.

### The Complexity of Analog Computation

We ask if analog computers can solve NP-complete problems efficiently. ... we choose not to try to implement (6.5), in order to avoid the introduction of the n new.by A VERGIS · 1986 · Cited by 207 · Related articles

### Lecture 4 1 Circuit Complexity

Lecture 4. Jonathan Katz. 1 Circuit Complexity. Circuits are directed, acyclic ... can be performed in depth O(log N(n)): to see this, note that the (i, j)th entry of ...by J Katz · Related articles

### On the Complexity of Parity Games

complexity of parity games (and in turn the µ-calculus model checking problem): that ... totality allow NP search problems to be grouped into complexity classes for ... W., and Wilke, T. (2002) Automata, Logics and Infinite Games: A Guide.

### a computational complexity perspective

the development of Computational Complexity Theory. While this mathematical ... Efficient computation and the class V. In all that follows, we focus on ... Note again that this conjecture 2.9 implies P = NP, but that it is independent of conjecture ...by A Wigderson · 2006 · Cited by 91 · Related articles

### an overview of computational complexity

the abstract complexity theory developed by Blum [6] and others. A second early ... by the computation time on multitape Turing machines was introduced, and ... which the number of processors is a resource bounded by a parameter H(n) (H is ...

### Barriers in Computational Complexity

May 1, 2013 — At the time, most of the techniques in complexity theory, if not all, were ... In fact, ACi stands for alternating class, and this alternation property ... that NPA ⊆ BPP ˜A, and an oracle and extension such that NEXP ˜A ⊆ P/Poly.