theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse...

In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a...

NthProofProvesComplexityFormula(i) and ComplexityLowerBoundNthProof(i) ≥ n return StringNthProof(i) Given an n, this procedure tries every proof until...

problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems...

who has made significant contributions to the fields of complexity theory and proof complexity. He is a university professor emeritus at the University...

computational complexity theory, a natural proof is a certain kind of proof establishing that one complexity class differs from another one. While these proofs are...

machines, interactive proof systems, Boolean circuits, and quantum computers). The study of the relationships between complexity classes is a major area...

structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research...

In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two...

major contributions to the fields of mathematical logic, complexity theory and proof complexity. He is currently a professor at the University of California...

In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem...

Ramanujan machine Computer-aided proof Formal verification Logic programming Proof checking Model checking Proof complexity Computer algebra system Program...

procedure will diverge (not terminate). Automated theorem proving Proof complexity Deductive system Willard Quine 1982 (1950). Methods of Logic. Harvard...

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete...

or by encoding their adjacency lists in binary. Even though some proofs of complexity-theoretic theorems regularly assume some concrete choice of input...

propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for proving...

Bernard A. Galler and Michael J. Fischer in 1964. In 1973, their time complexity was bounded to O ( log ∗ ⁡ ( n ) ) {\displaystyle O(\log ^{*}(n))} , the...

proof, a proof that can be verified by making a small number of queries to the bits of the proof Quantum complexity theory#Quantum query complexity,...

true Proof complexity, computational resources required to prove statements Proof procedure, method for producing proofs in proof theory Proof theory...

these systems. The characterization of standard complexity classes and correspondence to propositional proof systems allows to interpret theories of bounded...

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus...

In computational complexity theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin...

In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally...

focused on proof complexity, a branch of computational complexity theory that seeks upper and lower bounds on the lengths of mathematical proofs of logical...

of mathematical proofs could be automated. The relation between the complexity classes P and NP is studied in computational complexity theory, the part...

In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally...

Troelstra Predicative Arithmetic by Edward Nelson Logical Foundations of Proof Complexity by Stephen A. Cook and Phuong The Nguyen Bounded Reverse Mathematics...

between complexity and the logic of finite structures allows results to be transferred easily from one area to the other, facilitating new proof methods...

checkable proofs (proofs that can be checked by a randomized algorithm) of constant query complexity and logarithmic randomness complexity (uses a logarithmic...

In cryptography, a zero-knowledge proof (also known as a ZK proof or ZKP) is a protocol in which one party (the prover) can convince another party (the...