Linear constraints are mathematical conditions expressed as linear equations or inequalities that restrict the possible values of variables. These constraints define a feasible region within a problem space, typically a convex set. They are fundamental in optimization problems, where solutions must satisfy these straightforward relationships. Such restrictions are common in various computational models.
Context
In cryptographic proofs, particularly zero-knowledge proofs, linear constraints are utilized to represent the computational logic of a program in an arithmetic circuit. These constraints ensure the correctness of computations being verified. Efforts focus on optimizing the conversion of complex programs into minimal sets of linear constraints to improve proof generation efficiency.
Equifficient Polynomial Commitments introduce a new cryptographic primitive that separates linear and nonlinear constraints, setting the new frontier for zk-SNARK efficiency.
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