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Electronic Colloquium on Computational Complexity

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TR24-081 | 2nd April 2024
Sravanthi Chede, Leroy Chew, Anil Shukla

Circuits, Proofs and Propositional Model Counting

In this paper we present a new proof system framework CLIP (Cumulation Linear Induction Proposition) for propositional model counting. A CLIP proof firstly involves a circuit, calculating the cumulative function (or running count) of models counted up to a point, and secondly a propositional proof arguing for the correctness of ... more >>>

TR24-080 | 16th April 2024
Robert Andrews, Avi Wigderson

Constant-Depth Arithmetic Circuits for Linear Algebra Problems

We design polynomial size, constant depth (namely, $AC^0$) arithmetic formulae for the greatest common divisor (GCD) of two polynomials, as well as the related problems of the discriminant, resultant, Bézout coefficients, squarefree decomposition, and the inversion of structured matrices like Sylvester and Bézout matrices. Our GCD algorithm extends to any ... more >>>

TR24-079 | 20th April 2024
Tuomas Hakoniemi , Nutan Limaye, Iddo Tzameret

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers

Strong algebraic proof systems such as IPS (Ideal Proof System; Grochow-Pitassi JACM 2018) offer a general model for
deriving polynomials in an ideal and refuting unsatisfiable propositional formulas, subsuming most standard propositional proof systems. A major approach for lower bounding the size of IPS refutations is the Functional Lower Bound ... more >>>

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