
Lower bounds for prams over Z
This paper presents a new abstract method for proving lower bounds in co...
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Lower Bounds for the Happy Coloring Problems
In this paper, we study the Maximum Happy Vertices and the Maximum Happy...
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PRAMs over integers do not compute maxflow efficiently
Finding lower bounds in complexity theory has proven to be an extremely ...
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Hard QBFs for Merge Resolution
We prove the first proof size lower bounds for the proof system Merge Re...
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Proof Complexity of Symbolic QBF Reasoning
We introduce and investigate symbolic proof systems for Quantified Boole...
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FirstOrder Reasoning and Efficient SemiAlgebraic Proofs
Semialgebraic proof systems such as sumofsquares (SoS) have attracted...
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A formal proof of Hensel's lemma over the padic integers
The field of padic numbers Q_p and the ring of padic integers Z_p are ...
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SemiAlgebraic Proofs, IPS Lower Bounds and the τConjecture: Can a Natural Number be Negative?
We introduce the binary value principle which is a simple subsetsum instance expressing that a natural number written in binary cannot be negative, relating it to central problems in proof and algebraic complexity. We prove conditional superpolynomial lower bounds on the Ideal Proof System (IPS) refutation size of this instance, based on a wellknown hypothesis by Shub and Smale about the hardness of computing factorials, where IPS is the strong algebraic proof system introduced by Grochow and Pitassi (2018). Conversely, we show that short IPS refutations of this instance bridge the gap between sufficiently strong algebraic and semialgebraic proof systems. Our results extend to fullfledged IPS the paradigm introduced in Forbes et al. (2016), whereby lower bounds against subsystems of IPS were obtained using restricted algebraic circuit lower bounds, and demonstrate that the binary value principle captures the advantage of semialgebraic over algebraic reasoning, for sufficiently strong systems. Specifically, we show the following: (abstract continues in document.)
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