TL;DR
The Ideal Proof System, introduced by Grochow and Pitassi, is the focus of this talk, which will explore the IPS proof system, its connections to algebraic complexity, and recent developments in the area.
This paper investigates the question: what is a formal logical proof (in general—as opposed to: what is a formal proof in this or that specific proof system)? I begin by setting out a core conception of formal proof and substantiating its designation as ‘core’. The heart of this conception is that there must be an ef...
We give the simplest known algebraic proof of the PCP theorem, involving only ingredients like code concatenation, polynomial interpolation, and polynomial multiplication. Specifically, we prove that graph 3-coloring has a polynomial-sized proof that can be verified by a verifier tossing logarithmically many coins and...
This work proposes a proof calculus that captures the decision procedure for finite field reasoning employed by the SMT solver CVC 5 and instrumenting the solver to generate proofs within this calculus, and introduces an extension of the Practical Algebraic Calculus that mirrors the proposed system.
Pistis is introduced, an agentic, oracle-guided proof search that produces formal Lean proofs that satisfy faithfulness conditions and can accept or refute natural language proofs written by humans or AI, demonstrating that faithful formalization is useful as a proof-checking tool.
Relational program logics are a popular formalism for stating and proving properties that relate executions of several computations. We present Infinitary Relational Logic (IRL)—the first Hoare-style Separation Logic that allows one to state and prove relational properties of possibly infinite families of arbitrary pro...
The Ideal Membership Problem (IMP) asks whether a polynomial f belongs to an idealof Q[x_1, ..., x_n]. Polynomial Calculus (PC) certifies membership by deriving f from the generators, and a degree-d derivation needs at most n^O(d) steps. We write PC-IMPd for the problem of producing a degree-bounded PC certificate, and...
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