相关论文: Easy Sets and Hard Certificate Schemes

Consider the following two fundamental open problems in complexity theory: (a) Does a hard-on-average language in NP imply the existence of one-way functions?, or (b) Does a hard-on-average language in NP imply a hard-on-average problem in…

We build on a working program initiated by Pudl\'ak [Pud17] and construct an oracle relative to which each $\mathrm{coNP}$-complete set has $\mathrm{P}$-optimal proof systems and $\mathrm{NP}\cap\mathrm{coNP}$ does not have complete…

We investigate the complexity of explicit construction problems, where the goal is to produce a particular object of size $n$ possessing some pseudorandom property in time polynomial in $n$. We give overwhelming evidence that $\bf{APEPP}$,…

The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…

In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu [Comptes Rendus de l'Acad\'emie des Sciences-Series I-Mathematics, 328(6) (1999) pp.…

Probabilistically checkable proofs of proximity (PCPP) are proof systems where the verifier is given a 3SAT formula, but has only oracle access to an assignment and a proof. The verifier accepts a satisfying assignment with a valid proof,…

We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive…

We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just as with the natural proofs notion of Razborov and Rudich for boolean circuit lower bounds, our notion of algebraically natural lower bounds captures…

Supervised classification methods often assume that evaluation data is drawn from the same distribution as training data and that all classes are present for training. However, real-world classifiers must handle inputs that are far from the…

We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state…

We prove two sets of results concerning computational complexity classes. The first concerns a variation of the random oracle hypothesis posed by Bennett and Gill after they showed that relative to a randomly chosen oracle, P not equal NP…

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

An important tool for proving safety of dynamical systems is the notion of a barrier certificate. In this paper we prove that every robustly safe ordinary differential equation has a barrier certificate. Moreover, we show a construction of…

We investigate the complexity of $r$-Approval control problems in $k$-peaked elections, where at most $k$ peaks are allowed in each vote with respect to an order of the candidates. We show that most NP-hardness results in general elections…

We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…

We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…

Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

It was shown that adversarial examples improve object recognition. But what about their opposite side, easy examples? Easy examples are samples that the machine learning model classifies correctly with high confidence. In our paper, we are…

We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…