Algebraic Reductions of Knowledge
Algebraic Reductions of Knowledge
复制标题
DOI：
10.1007/978-3-031-38551-3_21
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Abhiram Kothapalli;Bryan Parno
中科院分区：
文献类型：
--
作者：
Abhiram Kothapalli;Bryan Parno
我们介绍reductions的知识，知识的参数，减少检查知识的证人在一个关系到检查知识的证人在另一个（更简单的）关系的一个概括。知识的约简统一了不断增长的现代技术，并提供了一个组合框架，以模块化方式推理复杂知识论证中的各个步骤。作为示范，我们简化和统一递归参数的线性代数语句分解为一个序列的知识减少。为了做到这一点，我们开发了知识的张量还原，它概括了许多递归参数共同的中央还原步骤。在张量知识约简的基础上，是一种新的信息论约简，它对于任何模U，
We introducereductions of knowledge, a generalization of arguments of knowledge, which reduce checking knowledge of a witness in one relation to checking knowledge of a witness in another (simpler) relation. Reductions of knowledge unify a growing class of modern techniques as well as provide a compositional framework to modularly reason about individual steps in complex arguments of knowledge. As a demonstration, we simplify and unify recursive arguments over linear algebraic statements by decomposing them as a sequence of reductions of knowledge. To do so, we develop thetensor reduction of knowledge, which generalizes the central reductive step common to many recursive arguments. Underlying the tensor reduction of knowledge is a new information-theoretic reduction, which, for any modulesU,, andsuch that, reduces the task of evaluating a homomorphism inUto evaluating a homomorphism inand evaluating a homomorphism in.