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 >>>

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 >>>

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 >>>

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 >>>

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 >>>