Smart Proofs via Smart Contracts: Succinct and Informative Mathematical
Derivations via Decentralized Markets
- URL: http://arxiv.org/abs/2102.03044v2
- Date: Mon, 8 Feb 2021 09:17:06 GMT
- Title: Smart Proofs via Smart Contracts: Succinct and Informative Mathematical
Derivations via Decentralized Markets
- Authors: Sylvain Carr\'e, Franck Gabriel, Cl\'ement Hongler, Gustavo Lacerda,
and Gloria Capano
- Abstract summary: SPRIG allows agents to propose and verify succinct and informative proofs in a decentralized fashion.
We show how agents with various types of information interact, leading to a proof tree with an appropriate level of detail.
We then analyze a simplified model, characterize its equilibria and compute the agents' level of trust.
- Score: 4.567122178196833
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Modern mathematics is built on the idea that proofs should be translatable
into formal proofs, whose validity is an objective question, decidable by a
computer. Yet, in practice, proofs are informal and may omit many details. An
agent considers a proof valid if they trust that it could be expanded into a
machine-verifiable proof. A proof's validity can thus become a subjective
matter and lead to a debate, which may be difficult to settle. Hence, while the
concept of valid proof is well-defined, the process to establish validity is
itself a complex multi-agent problem.
We introduce the SPRIG protocol. SPRIG allows agents to propose and verify
succinct and informative proofs in a decentralized fashion; the trust is
established by agents being able to request more details in the proof steps;
debates, if they arise, must isolate details of proofs and, if they persist, go
down to machine-level details, where they are automatically settled. A
structure of bounties and stakes is set to incentivize agents to act in good
faith.
We propose a game-theoretic discussion of SPRIG, showing how agents with
various types of information interact, leading to a proof tree with an
appropriate level of detail and to the invalidation of wrong proofs, and we
discuss resilience against various attacks. We then analyze a simplified model,
characterize its equilibria and compute the agents' level of trust.
SPRIG is designed to run as a smart contract on a blockchain platform. This
allows anonymous agents to participate in the verification debate, and to
contribute with their information. The smart contract mediates the
interactions, settles debates, and guarantees that bounties and stakes are paid
as specified.
SPRIG enables new applications, such as the issuance of bounties for open
problems, and the creation of derivatives markets, allowing agents to inject
more information pertaining to proofs.
Related papers
- Towards Secure and Trusted-by-Design Smart Contracts [0.3499870393443268]
Evidential transactions involve the exchange of any form of physical evidence, such as money, birth certificate, visas, tickets, etc.
Most of the time, evidential transactions occur in the context of complex procedures, called evidential protocols, among physical agents.
The blockchain provides the mechanisms to transfer evidence, while smart contracts allow encoding evidential protocols on top of a blockchain.
As a smart contract foregoes trusted third-parties and runs on several machines anonymously, it constitutes a highly critical program that has to be secure and trusted-by-design.
arXiv Detail & Related papers (2024-03-25T16:14:22Z) - Neuro-Symbolic Integration Brings Causal and Reliable Reasoning Proofs [102.00359477458029]
We present a neuro-symbolic integration method, in which a neural LLM is used to represent the knowledge of the problem.
An LLM-free symbolic solver is adopted to do deliberative reasoning using the knowledge.
arXiv Detail & Related papers (2023-11-16T11:26:21Z) - Unclonable Non-Interactive Zero-Knowledge [13.011345529764787]
A non-interactive ZK (NIZK) proof enables verification of NP statements without revealing secrets about them.
In this paper, we ask whether it is possible to rely on quantum information in order to build NIZK proof systems that are impossible to clone.
arXiv Detail & Related papers (2023-10-11T01:32:36Z) - CryptoVampire: Automated Reasoning for the Complete Symbolic Attacker Cryptographic Model [8.838422697156195]
We introduce the CryptoVampire cryptographic protocol verifier, which for the first time fully automates proofs of trace properties in the BC Logic.
Key technical contribution is a first-order (FO) formalization of protocol properties with tailored handling of subterm relations.
On the theoretical side, we restrict full FO logic with cryptographic axioms to ensure that, by losing the expressivity of the HO BC Logic, we do not lose soundness.
arXiv Detail & Related papers (2023-05-20T11:26:51Z) - Generating Natural Language Proofs with Verifier-Guided Search [74.9614610172561]
We present a novel stepwise method NLProofS (Natural Language Proof Search)
NLProofS learns to generate relevant steps conditioning on the hypothesis.
It achieves state-of-the-art performance on EntailmentBank and RuleTaker.
arXiv Detail & Related papers (2022-05-25T02:22:30Z) - Synthetic Disinformation Attacks on Automated Fact Verification Systems [53.011635547834025]
We explore the sensitivity of automated fact-checkers to synthetic adversarial evidence in two simulated settings.
We show that these systems suffer significant performance drops against these attacks.
We discuss the growing threat of modern NLG systems as generators of disinformation.
arXiv Detail & Related papers (2022-02-18T19:01:01Z) - multiPRover: Generating Multiple Proofs for Improved Interpretability in
Rule Reasoning [73.09791959325204]
We focus on a type of linguistic formal reasoning where the goal is to reason over explicit knowledge in the form of natural language facts and rules.
A recent work, named PRover, performs such reasoning by answering a question and also generating a proof graph that explains the answer.
In our work, we address a new and challenging problem of generating multiple proof graphs for reasoning over natural language rule-bases.
arXiv Detail & Related papers (2021-06-02T17:58:35Z) - Experimental relativistic zero-knowledge proofs [4.334542470441071]
We develop a zero-knowledge protocol involving two separated verifier-prover pairs.
Security is enforced via the physical principle of special relativity.
This demonstrates the practical potential of multi-prover zero-knowledge protocols.
arXiv Detail & Related papers (2020-12-18T19:00:01Z) - PRover: Proof Generation for Interpretable Reasoning over Rules [81.40404921232192]
We propose a transformer-based model that answers binary questions over rule-bases and generates the corresponding proofs.
Our model learns to predict nodes and edges corresponding to proof graphs in an efficient constrained training paradigm.
We conduct experiments on synthetic, hand-authored, and human-paraphrased rule-bases to show promising results for QA and proof generation.
arXiv Detail & Related papers (2020-10-06T15:47:53Z) - Empirically Verifying Hypotheses Using Reinforcement Learning [58.09414653169534]
This paper formulates hypothesis verification as an RL problem.
We aim to build an agent that, given a hypothesis about the dynamics of the world, can take actions to generate observations which can help predict whether the hypothesis is true or false.
arXiv Detail & Related papers (2020-06-29T01:01:10Z) - SNARKs to the rescue: proof-of-contact in zero knowledge [0.0]
This paper describes techniques to help with COVID-19 automated contact tracing, and with the restoration efforts.
We describe a decentralized protocol for proof-of-contact'' in zero knowledge where a person can publish a short cryptographic proof attesting to the fact that they have been infected.
arXiv Detail & Related papers (2020-05-26T13:00:37Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.