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Abstract machine that models computation
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two
Interactive_proof_system
Topics referred to by the same term
Interactive proof can refer to: The abstract concept of an Interactive proof system Interactive theorem proving software This disambiguation page lists
Interactive_proof
Proving validity without revealing other data
zero-knowledge proof, should nonetheless remain unable to prove the statement to further third parties. Zero-knowledge proofs can be interactive, meaning that
Zero-knowledge_proof
Interactive theorem prover software
mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration
Proof_assistant
Cryptographic primitive
Non-interactive zero-knowledge proofs are cryptographic primitives, where information between a prover and a verifier can be authenticated by the prover
Non-interactive zero-knowledge proof
Non-interactive_zero-knowledge_proof
Class of interactive proof
In cryptography, a proof of knowledge is an interactive proof in which the prover succeeds in 'convincing' a verifier that the prover knows something.
Proof_of_knowledge
Placeholder characters
the genders are alternated: Alice, Bob, Carol, Dave, Eve, etc. For interactive proof systems there are other characters: The names Alice and Bob are often
Alice_and_Bob
Cryptographic technique
heuristic, or Fiat–Shamir transformation, is a technique for taking an interactive proof of knowledge and creating a digital signature based on it. This way
Fiat–Shamir_heuristic
Israeli American computer scientist (born 1959)
additional knowledge. They began by studying interactive proofs more broadly, where a proof is developed interactively by answering a series of questions about
Shafi_Goldwasser
sum-check protocol is a cryptographic protocol for the construction of interactive proof systems, used widely in zero-knowledge protocols. The sum-check protocol
Sum-check_protocol
American cryptographer (born 1974)
Jens Groth, "Efficient Non-interactive Proof Systems for Bilinear Groups," introduced a new type of non-interactive proof system offering improved efficiency
Amit_Sahai
Set of problems in computational complexity theory
classes defined using interactive proof systems include MIP (multiprover interactive polynomial time) and QIP (quantum interactive polynomial time). An
Complexity_class
Proof assistant
Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical checking of proofs of these
Rocq
Complexity class from interactive proofs
theory, the class IP (which stands for interactive proof) is the class of problems solvable by an interactive proof system. It is equal to the class PSPACE
IP_(complexity)
Theorem in computational complexity theory
work on interactive proofs and probabilistically checkable proofs. The first theorem relating standard proofs and probabilistically checkable proofs is the
PCP_theorem
Interactive proof system in computational complexity theory
theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin tosses are constrained to be public
Arthur–Merlin_protocol
Test to determine whether a user is human
on 2 October 2013. Retrieved 28 September 2013. "Asirra is a human interactive proof that asks users to identify photos of cats and dogs". Microsoft. Archived
CAPTCHA
American computer scientist
1980s on the invention of interactive proof systems, where a proof could be developed by answering a series of interactive questions between different
Charles_Rackoff
to 3/4. A quantum interactive proof with two competing provers is a generalization of the single prover quantum interactive proof system. It can be modelled
Quantum_refereed_game
Mathematical proof at least partially generated by computer
new proofs for known theorems.[citation needed] Additionally, interactive proof assistants allow mathematicians to develop human-readable proofs which
Computer-assisted_proof
Italian-American computer scientist (born 1954)
invented interactive proofs in the 1980s, at the same time as László Babai and Shlomo Moran. In an interactive proof system, participants develop a proof by
Silvio_Micali
Complexity class
Quantum Interactive Proof) is the quantum computing analogue of the classical complexity class IP, which is the set of problems solvable by an interactive proof
QIP_(complexity)
Computer science award
S.; Micali, S.; Rackoff, C. (1989), "The knowledge complexity of interactive proof systems" (PDF), SIAM Journal on Computing, 18 (1): 186–208, CiteSeerX 10
Gödel_Prize
Australian computer scientist
Previously he has worked on formal specification, interactive proof, automated verification and proof description languages. He holds a Ph.D. from the
Don_Syme
Software for automated theorem proving
IsaPlanner is a proof planner for the interactive proof assistant, Isabelle, originally developed by Lucas Dixon. IsaPlanner 2: A Proof Planner in Isabelle
IsaPlanner
American computer scientist (born 1963)
scientist known for major results in computational complexity and interactive proof systems. Since 2019, he has been at the Illinois Institute of Technology
Lance_Fortnow
Topics referred to by the same term
determine a material's porous structure MIP, an interactive proof system complexity class; see Interactive proof system Minimum ionizing particle, in particle
MIP
Practice and study of secure communication techniques
'theoretical'[clarification needed] cryptosystems include interactive proof systems, (like zero-knowledge proofs) and systems for secret sharing. Lightweight cryptography
Cryptography
System that regulates the formation of blocks on a blockchain
Proof of work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the
Proof_of_work
Establishment of a theorem using inference from the axioms
sequence. Formal proofs often are constructed with the help of computers in interactive theorem proving (e.g., through the use of proof checker and automated
Formal_proof
Israeli computer scientist
well known for his work on interactive proof systems. His two most-cited papers are Raz (1998) on multi-prover interactive proofs and Raz & Safra (1997) on
Ran_Raz
Abstract machine used to study decision problems
box (i.e., as a random oracle). Black box group Turing reduction Interactive proof system Matroid oracle Demand oracle Padding oracle attack van Melkebeek
Oracle_machine
Concept in computational complexity theory
two provers gives it great power. See interactive proof system#MIP for more details. Another interactive proof system characterizing NEXPTIME is a certain
NEXPTIME
Theoretical computer scientist
and quantum computation. He is well known for his work on quantum interactive proofs, and the quantum analogue of the celebrated result IP = PSPACE: QIP = PSPACE
John Watrous (computer scientist)
John_Watrous_(computer_scientist)
Class of computational complexity
be characterized as all the languages recognizable by a particular interactive proof system, the one defining the class IP. In this system, there is an
PSPACE
Functional programming language
PhD Thesis. Chalmers University of Technology, 2007. [1] "Agda: An Interactive Proof Editor". Archived from the original on 8 October 2011. Retrieved 20
Agda_(programming_language)
Israeli computer scientist
the computational complexity of pseudorandom number generators, and interactive proof systems, among other topics. Nisan won an ACM Distinguished Dissertation
Noam_Nisan
Greek mathematician and logician (born 1947)
work on randomized complexity classes, Arthur–Merlin protocols, and interactive proof systems has been very influential in proving important theorems and
Stathis_Zachos
Hungarian-American mathematician and computer scientist
academic papers. His notable accomplishments include the introduction of interactive proof systems, the introduction of the term Las Vegas algorithm, and the
László_Babai
Mathematical model of computation
computation is also critical for the definition of most classes of interactive proof systems, in which the verifier machine depends on randomness to avoid
Probabilistic_Turing_machine
Type of computational problem
complexity classes of P, NP, PH, etc, in circuit complexity, and in interactive proof systems. Let R be a search problem, formalised as a binary relation
Counting_problem_(complexity)
Computational Formula that can be measured in terms of True or False
seminal result IP = PSPACE was shown (see interactive proof system), it was done by exhibiting an interactive proof system that could solve QBF by solving
True quantified Boolean formula
True_quantified_Boolean_formula
Complexity class used to classify decision problems
NP can be seen as a very simple type of interactive proof system, where the prover comes up with the proof certificate and the verifier is a deterministic
NP_(complexity)
platform that supports Qt) Proofs: No Extra: Editable Live Geometry is a free CodePlex project that lets you create interactive ruler and compass constructions
List of interactive geometry software
List_of_interactive_geometry_software
Inherent difficulty of computational problems
(not decision problems). Classes like IP and AM are defined using Interactive proof systems. ALL is the class of all decision problems. For the complexity
Computational complexity theory
Computational_complexity_theory
Realization of a certain method or idea in order to demonstrate its feasibility
A proof of concept (POC or PoC), also known as proof of principle, is an inchoate realization of a certain idea or method in order to demonstrate its feasibility
Proof_of_concept
Concept in cryptography
+ x 7 {\displaystyle f_{2}=x+x^{7}} , t = 6 {\displaystyle t=6} Interactive proof: The following 5 steps verify the integrity of the dealer to the Share
Verifiable_secret_sharing
Programming language
theorem provers to discharge VCs. Use of other provers (including interactive proof checkers) is also possible through other components of the Why3 toolset
SPARK_(programming_language)
Nonconstructive method for mathematical proofs
Mathematics portal Interactive proof system Las Vegas algorithm Incompressibility method Method of conditional probabilities Probabilistic proofs of non-probabilistic
Probabilistic_method
Cryptographic proof technique
with n-bit output. Interactive proof system Universal composability Bellare, Mihir, and Phillip Rogaway. "Code-based game-playing proofs and the security
Hybrid argument (cryptography)
Hybrid_argument_(cryptography)
Term in logic and deductive reasoning
completeness proof applies to all classical models, not some special proper subclass of intended ones. Philosophy portal Soundness (interactive proof) Type soundness
Soundness
Branch of mathematical logic
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,
Proof_theory
(TPMs), interactive proofs, probabilistically checkable proofs, efficient arguments, and Micali's CS proofs. These verifications are either interactive which
Verifiable_computing
American theoretical computer scientist (born 1954)
complexity theory, specifically efficient error correcting codes, interactive proof systems, randomness, quantum computation, and establishing the inherent
Michael_Sipser
Israeli computer scientist
and Charles Rackoff for their work on Arthur–Merlin protocols and interactive proof systems. Faculty profile, the Technion, retrieved 2010-12-02. Shlomo
Shlomo_Moran
integer determinant of a matrix IP Solvable in polynomial time by an interactive proof system L Solvable with logarithmic (small) space LOGCFL Logspace-reducible
List_of_complexity_classes
Proof that a number is prime
and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality
Primality_certificate
American mathematician
Fellowship. As a student of Umesh Vazirani at Berkeley, Mahadev discovered interactive proof systems that could demonstrate with high certainty, to an observer
Urmila_Mahadev
Retrieved 14 August 2011. Paulson, Lawrence C. (2008). "Automation for Interactive Proof: Techniques, Lessons and Prospects" (PDF). Tools and Techniques for
E_(theorem_prover)
Quantum Merlin Arthur
S2CID 6869749. Watrous, John (2003). "PSPACE has constant-round quantum interactive proof systems". Theoretical Computer Science. 292 (3): 575–588. doi:10
QMA
verification of mathematical proofs in complexity theory"; recipient of the Gödel Prize in 1993 "for the development of interactive proof systems" Ford Professor
List of University of California, Berkeley alumni
List_of_University_of_California,_Berkeley_alumni
Problem a computer might be able to solve
complexity, including hardness of approximation, property testing, and interactive proof systems. Lateral computing, alternative approaches to solving problems
Computational_problem
Proof assistant and programming language
Lean is a proof assistant and a functional programming language. It is based on the calculus of constructions with inductive types. It is a free and open-source
Lean_(proof_assistant)
Danish computer scientist (born 1963)
characterizing complexity classes such as PSPACE and NEXPTIME in terms of interactive proof systems; this work became part of his 1991 Ph.D. thesis from the University
Carsten_Lund
Mathematical theory of data types
Much of the current research into type theory is driven by proof checkers, interactive proof assistants, and automated theorem provers. Most of these systems
Type_theory
Type of consensus algorithm
Proof of space (PoS) is a type of consensus algorithm achieved by demonstrating one's legitimate interest in a service (such as sending an email) by allocating
Proof_of_space
Formal language and associated computer program
language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have
Metamath
Set of problems solved by small circuits
_{2}^{\mathsf {P}}} , even PSPACE = MA. Proof: Consider a language L from PSPACE. It is known that there exists an interactive proof system for L, where actions of
P/poly
Designed to be proof against misuse or error
(link) Wasserman, Anthony I. (1973-06-04). "The design of 'idiot-proof' interactive programs". Proceedings of the June 4-8, 1973, national computer conference
Idiot-proof
Concept in computer science
structures found in device drivers). Interactive Proof. Proofs have been done using embeddings of Separation Logic into interactive theorem provers such as Rocq
Separation_logic
2026 action-adventure video game
adaptations. IO Interactive announced the development of a James Bond game in November 2020. The game entered full production at IO Interactive following the
007_First_Light
Mathematical proof Direct proof Reductio ad absurdum Proof by exhaustion Constructive proof Nonconstructive proof Tautology Consistency proof Arithmetization
List of mathematical logic topics
List_of_mathematical_logic_topics
Higher-order logic (HOL) automated theorem prover
Isabelle/ZF. Isabelle's main proof method is a higher-order version of resolution, based on higher-order unification. Though interactive, Isabelle features efficient
Isabelle_(proof_assistant)
Proof assistant
At the interactive level, the system implements a small step execution of structured tactics allowing a much better management of the proof development
Matita
Theorem concerning quantum field theory ground states
applies to any eigenstate of the Hamiltonian. Its proof relies on the concept of starting with a non-interacting Hamiltonian and adiabatically switching on the
Gell-Mann_and_Low_theorem
Cryptographic protocol for two-party computation
Micali, S; Rackoff, C (1985-12-01). "The knowledge complexity of interactive proof-systems". Proceedings of the seventeenth annual ACM symposium on Theory
Garbled_circuit
Mathematics award
contribution to understanding the paradoxical term "zero-knowledge interactive proofs". 1998 Peter Shor "For his outstanding work on quantum computation
IMU_Abacus_Medal
Centers of the incircles of triangles inside a cyclic quadrilateral form a rectangle
(1976). "几何学辞典: 问题解法". Archive.org. Problem 587. Japanese theorem, interactive proof with animation Dynamic Geometry Sketch, Cyclic Quadrilateral Incentres
Japanese theorem for cyclic quadrilaterals
Japanese_theorem_for_cyclic_quadrilaterals
Interactive theorem proving systems
Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Berlin, Heidelberg: Springer-Verlag. ISBN 978-3-540-45949-1. "HOL Interactive Theorem Prover"
HOL_(proof_assistant)
Method of software development
code". GitHub. Abrial, J.-R.; Cansell, D. (2003). "Click'n Prove: Interactive Proofs within Set Theory". In Basin, D.; Wolff, B. (eds.). Theorem Proving
B-Method
American live-streaming platform
Curse, from Twitch Interactive for an undisclosed amount. Curse was dissolved and its assets were moved under Twitch Interactive. Twitch's new headquarters
Twitch_(service)
Swiss film director
that he now applied to movies. He shot an interactive proof of concept film in 2013 and set up interactive movie technology company CtrlMovie AG the year
Tobias_Weber
Topics referred to by the same term
knowledge in cryptology Zero-knowledge proof Non-interactive zero-knowledge proof Zero-knowledge password proof 0K, an abbreviation for zero keel, a type
0K
American consultant and deputy mayor
The Planning Report". www.planningreport.com. Retrieved 2018-08-06. Interactive, Proof. "Downtown LA - Innovate DTLA". www.downtownla.com. Retrieved 2018-08-06
Amanda_Daflos
Academic journal
1987 Boppana, R.B., Hastad, J., Zachos, S., Does co-NP have short interactive proofs?, 1987 Korel, B., Laski, J., Dynamic program slicing, 1988 Kamada
Information Processing Letters
Information_Processing_Letters
focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and
Focused_proof
cryptologist, won the Godel Prize for his work on interactive proof systems and zero-knowledge proofs Geoffrey Hinton (professor of computer science, 1987–98
List of University of Toronto faculty
List_of_University_of_Toronto_faculty
Jigoro often hurl at him) and she is destined for much greater things. As proof, his father asks if he has "made it" with Yawara, or even kissed her or
List_of_Yawara!_episodes
American computer scientist (born 1946)
satisfies the constraints. This result even led to the breakthroughs of interactive proof systems Karloff-Nisan and Shamir, including the result IP = PSPACE
Richard_Lipton
algorithm Non-determinism Non-deterministic Turing machine Interactive computation Interactive proof system Probabilistic Turing Machine Approximation algorithm
List of computability and complexity topics
List_of_computability_and_complexity_topics
Cryptographer
Massachusetts Institute of Technology (PhD) Thesis Randomness in Interactive Proofs (1991) Doctoral advisor Silvio Micali Academic work Discipline Computer
Mihir_Bellare
him. Nolan is shot during her arrest, but survived thanks to his bullet-proof vest. The story is told as an in-work documentary, with character interviews
List_of_The_Rookie_episodes
Israeli computer scientist
science for his papers "Interactive Proofs and the Hardness of Approximating Cliques" and "Probabilistic Checking of Proofs: A New Characterization of
Shmuel_Safra
Planar maps require at most four colors
this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained
Four_color_theorem
Micali, S; Rackoff, C (1985-12-01). "The knowledge complexity of interactive proof-systems". Proceedings of the seventeenth annual ACM symposium on Theory
Secure_two-party_computation
borrowing her car and trashing it. Clover denies both accusations, but the proof seems to be irrefutable. In fact, Sam and Alex are so miffed that they request
List of Totally Spies! episodes
List_of_Totally_Spies!_episodes
American basketball player (born 1984)
MVP?". ESPN Insider. Retrieved December 22, 2021. Partnow, Seth. "Here's proof LeBron James is exiting the prime of his career". The Washington Post. Retrieved
LeBron_James
Film by Curry Barker
would "definitely recommend" it. Christian Zilko of IndieWire said it was "proof that the Cregger-ification of 2020s horror is in full effect, as its combination
Obsession_(2025_film)
List of episodes of the TV show Blindspot
Weller. Meanwhile, Keaton awakens from his coma. He tells Zapata that he has proof of everything that he had tasked her with, which could clear her name, though
List_of_Blindspot_episodes
Concept in computer science
"Mechanical Verification of a Constructive Proof for FLP", in Blanchette, Jasmin Christian; Merz, Stephan (eds.), Interactive Theorem Proving, Lecture Notes in
Consensus_(computer_science)
INTERACTIVE PROOF
INTERACTIVE PROOF
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Girl/Female
Muslim
Guide, Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Indian
Proof
Girl/Female
Muslim
Proof
Boy/Male
Indian
Proof
Girl/Female
Biblical
Flight, proof, temptation, delicate.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Good Looking; Interactive; Brightness
Boy/Male
Muslim
Proof
Boy/Male
Muslim
Evidence. Proof.
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Arabic, Muslim
Evidence; Proof
Surname or Lastname
English
English : from Middle English, Old French palmer, paumer (from palme, paume ‘palm tree’, Latin palma), a nickname for someone who had been on a pilgrimage to the Holy Land. Such pilgrims generally brought back a palm branch as proof that they had actually made the journey, but there was a vigorous trade in false souvenirs, and the term also came to be applied to a cleric who sold indulgences.Swedish (Palmér) : ornamental name formed with palm ‘palm tree’ + the suffix -ér, from Latin -erius ‘descendant of’.Irish : when not truly of English origin (see 1 above), a surname adopted by bearers of Gaelic Ó Maolfhoghmhair (see Milford) perhaps because they were from an ecclesiastical family.German : topographic name for someone living among pussy willows (see Palm 2).German : from the personal name Palm (see Palm 3).
Boy/Male
Muslim
Argument, Reasoning, Proof
Boy/Male
Indian
Argument, Reasoning, Proof
Boy/Male
Muslim
Proof
Boy/Male
Arabic, Muslim
Another Name for God; Evidence; Proof
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu, Traditional
Witness; Justice; Proof; Cute Princess; Loved by Everyone; Grace; Purity; Pluck; Witness Truth; Queen; Princess; Real; Truth
Girl/Female
Indian
Witness; Proof
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
INTERACTIVE PROOF
INTERACTIVE PROOF
Girl/Female
Hindu
Knowledge or wisdom
Boy/Male
Hindu, Indian
Sun God
Girl/Female
Hebrew
He shall add.
Boy/Male
Tamil
Alias name of Lord Shiva
Boy/Male
Russian
Stone.
Girl/Female
Indian
Tall and pretty
Boy/Male
Arabic
Scrupulously Clean; Refined; Most Noble; Excellent
Girl/Female
Hindu
Saisudha, Early morning, Dawn
Boy/Male
Hindu, Indian, Punjabi, Sikh
Horizon
Boy/Male
Hindu, Indian
Sunshine
INTERACTIVE PROOF
INTERACTIVE PROOF
INTERACTIVE PROOF
INTERACTIVE PROOF
INTERACTIVE PROOF
n.
The quality or state of being valid; strength; force; especially, power to convince; justness; soundness; as, the validity of an argument or proof; the validity of an objection.
a.
Cleaving or sticking like wax.
n.
Mutual or reciprocal action or influence; as, the interaction of the heart and lungs on each other.
a.
Having the power to prohibit; as, an interdictive sentence.
a.
Repeating.
n.
The iterative sound of beating a drum, or of a galloping horse.
v. t.
Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.
n.
Mutual action or influence; interaction; as, the interplay of affection.
n.
A trial impression, as from type, taken for correction or examination; -- called also proof sheet.
a.
Not tractile; incapable of being drawn out or extended.
v. t.
To arm with proof armor; to arm securely; as, to proof-arm herself.
n.
Intermediate action.
a.
Used in proving or testing; as, a proof load, or proof charge.
a.
Made and operated by interaction of forces without a directing intelligence; as, a mechanical universe.
a.
Firm or successful in resisting; as, proof against harm; waterproof; bombproof.
n.
The quality of correlation; reciprocation; interchange; interaction; interdependence.
a.
Highly rectified; very strongly alcoholic; as, high-proof spirits.
n.
A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, -- as between the writ and the declaration, or between the allegation and the proof.
n.
An effect of the interaction of the actions of two agents such that the result of the combined action is greater than expected as a simple additive combination of the two agents acting separately. Also synergism.
a.
Proof against proofs; obstinate in the wrong.