1
In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded algebra with an added chain complex structure that respects the algebra structure.
== Definition ==
A differential graded algebra (or simply DG-algebra) A is a graded algebra equipped with a map
d
:
A
→
A
{\displaystyle d\colon A\to A}
which is either degree 1 (cochain complex convention) or degree
−
1
{\displaystyle -1}
(chain complex convention) that satisfies t...
In computational complexity theory, the class IP (which stands for Interactive Polynomial time) is the class of problems solvable by an interactive proof system. It is equal to the class PSPACE. The result is a famous example where the proof does not relativize.
The concept of an interactive proof system was first introduced by Shafi Goldwasser, Silvio Micali, and Charles Rackoff in 1985. An interactive proof system consists of two machines, a prover, P, which presents a proof that a given string n is a member of some language, and a verifier, V, that checks that the presented proof is correct...
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties. The parties, the verifier and the prover, interact by exchanging messages in order to ascertain whether a given string belongs to a language or not. The prover is all-powerful and possesses unlimited computational resources, but cannot be trusted, while the verifier has bounded computation power. Messages are sent between the verifier and prover until the verifier has an answer to the problem and has "convinced" itself that it is correct...
Consider AM the class of languages with an interactive proof with public coins of two rounds (known as Arturo-Merlin proof).
We say $L\le_r M$ if there is a probabilistic Turing machine $P$ s.t. $\forall w,\mathbb{P}(L(w)=M(P(w)))\ge \frac{2}{3}$
Then, given a class of complexity $C$ with a co...
