Complexity theory verifier

What is a certificate for a verifier?
A certificate is often thought of as a solution path within a verification process, which is used to check whether a problem gives the answer "Yes" or "No"..
What is a verifier algorithm?
A verification algorithm is a two-argument algorithm A, where one argument is an ordinary input string x, and the other argument is a binary string y called a certificate.
Algorithm A verifies x if there exists a y such that A(x,y) = 1..
What is a verifier in complexity theory?
A verifier for a language L is a TM V with the following properties: ● V is a decider (that is, V halts on all inputs.) ● For any string w ∈ Σ*, the following is true: w ∈ L iff ∃c ∈ Σ*..
In computational complexity theory, a certificate (also called a witness) is a string that certifies the answer to a computation, or certifies the membership of some string in a language.

Jul 4, 2018A verifier for a language L is an algorithm that accepts as input an instance x of A and a witness w, and has the following properties:.What is the difference between "Decision" and "Verification" in Is the verifier for an $NP$ and its $co-NP$ the same?Verifier for A_tm in polynomial time - how to formally prove it does Verifiers equivalent classes - Computer Science Stack ExchangeMore results from cs.stackexchange.com

Jul 4, 2018A verifier for a language L is an algorithm that accepts as input an instance x of A and a witness w, and has the following properties:.What is the difference between "Decision" and "Verification" in Is the verifier for an $NP$ and its $co-NP$ the same?What is a witness string? I unable to understand the conceptUnderstanding this verifier runs in plynomial timeMore results from cs.stackexchange.com

Jul 4, 2018A verifier for a language L is an algorithm that accepts as input an instance x of A and a witness w, and has the following properties:.What is the difference between "Decision" and "Verification" in What is a witness string? I unable to understand the conceptUnderstanding this verifier runs in plynomial timeVerifier for A_tm in polynomial time - how to formally prove it does More results from cs.stackexchange.com

A verifier for a language L is a TM V with the following properties: V is a decider (that is, V halts on all inputs.) If w ∈ L, a string c for which V accepts ⟨w, c⟩ is called a certificate for c. V is required to halt, so given any potential certificate c for w, you can check whether the certificate is correct.

In computational complexity theory, the class QIP is the quantum computing analogue of the classical complexity class IP, which is the set of problems solvable by an interactive proof system with a polynomial-time verifier and one computationally unbounded prover.
Informally, IP is the set of languages for which a computationally unbounded prover can convince a polynomial-time verifier to accept when the input is in the language and cannot convince the verifier to accept when the input is not in the language.
In other words, the prover and verifier may interact for polynomially many rounds, and if the input is in the language the verifier should accept with probability greater than 2/3, and if the input is not in the language, the verifier should be reject with probability greater than 2/3.
In IP, the verifier is like a BPP machine.
In QIP, the communication between the prover and verifier is quantum, and the verifier can perform quantum computation.
In this case the verifier is like a BQP machine.

Systems capable of proving their own consistency

Self-verifying theories are consistent first-order systems of arithmetic, much weaker than Peano arithmetic, that are capable of proving their own consistency.
Dan Willard was the first to investigate their properties, and he has described a family of such systems.
According to Gödel's incompleteness theorem, these systems cannot contain the theory of Peano arithmetic nor its weak fragment Robinson arithmetic; nonetheless, they can contain strong theorems.

In complexity theory, UP is the complexity class of decision problems solvable in polynomial time on an unambiguous Turing machine with at most one accepting path for each input. UP contains P and is contained in NP.

Concept in computer science

Complexity theory verifier

What is a certificate for a verifier?

What is a verifier algorithm?

What is a verifier in complexity theory?