Sanjeev Arora, Madhu Sudan

NP = PCP(log n, 1) and related results crucially depend upon

the close connection between the probability with which a

function passes a ``low degree test'' and the distance of

this function to the nearest degree d polynomial. In this

paper we study a test ...
more >>>

Venkatesan Guruswami

We prove hardness results for approximating set splitting problems and

also instances of satisfiability problems which have no ``mixed'' clauses,

i.e all clauses have either all their literals unnegated or all of them

negated. Recent results of Hastad imply tight hardness results for set

splitting when all sets ...
more >>>

Alessandro Chiesa, Michael Forbes, Nicholas Spooner

Many seminal results in Interactive Proofs (IPs) use algebraic techniques based on low-degree polynomials, the study of which is pervasive in theoretical computer science. Unfortunately, known methods for endowing such proofs with zero knowledge guarantees do not retain this rich algebraic structure.

In this work, we develop algebraic techniques for ... more >>>

Orr Paradise

Probabilistically checkable proofs (PCPs) can be verified based only on a constant amount of random queries, such that any correct claim has a proof that is always accepted, and incorrect claims are rejected with high probability (regardless of the given alleged proof). We consider two possible features of PCPs:

- ...
more >>>

Shuichi Hirahara, Naoto Ohsaka

In the Minmax Set Cover Reconfiguration problem, given a set system $\mathcal{F}$ over a universe and its two covers $\mathcal{C}^\mathrm{start}$ and $\mathcal{C}^\mathrm{goal}$ of size $k$, we wish to transform $\mathcal{C}^\mathrm{start}$ into $\mathcal{C}^\mathrm{goal}$ by repeatedly adding or removing a single set of $\mathcal{F}$ while covering the universe in any intermediate state. ... more >>>