Related papers: Polynomial-Time Multi-Selectivity
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
Persistence is a strong, global, behavioural property of a Petri net, meaning that no activity can disable a different activity. Persistent permutability is a weaker property, pertaining to individual interleavings of a Petri net and…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
We answer one of the main questions in generalized descriptive set theory, the Friedman-Hyttinen-Kulikov conjecture on the Borel reducibility of the Main Gap. We show a correlation between Shelah's Main Gap and generalized Borel…
Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…
A set is autoreducible if it can be reduced to itself by a Turing machine that does not ask its own input to the oracle. We use autoreducibility to separate the polynomial-time hierarchy from polynomial space by showing that all…
In this paper we study a polynomial time algorithms that for an input $A\subseteq {B_m}$ outputs a decision tree for $A$ of minimum depth. This problem has many applications that include, to name a few, computer vision, group testing, exact…
A categorical point of view about minimization in subrecursive classes is presented by extending the concept of Symmetric Monoidal Comprehension to that of Distributive Minimization Comprehension. This is achieved by endowing the former…
Abstract State Machines (ASMs) provide a model of computations on structures rather than strings. Blass, Gurevich and Shelah showed that deterministic PTIME-bounded ASMs define the choiceless fragment of PTIME, but cannot capture PTIME. In…
Motivated by applications where impatience is pervasive and evaluation times are uncertain, we study a selection model where options may expire at an unknown point in time and evaluation times are stochastic. Initially, the decision-maker…
In [2], the authors prove Stillman's conjecture in all characteristics and all degrees by showing that, independent of the algebraically closed field $K$ or the number of variables, $n$ forms of degree at most $d$ in a polynomial ring $R$…
We examine some combinatorial properties of parallel cut elimination in multiplicative linear logic (MLL) proof nets. We show that, provided we impose a constraint on some paths, we can bound the size of all the nets satisfying this…
We say that a topological space X is selectively sequentially pseudocompact (SSP for short) if for every sequence (U_n) of non-empty open subsets of X, one can choose a point x_n in U_n for every n in such a way that the sequence (x_n) has…
This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially…
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…
In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that…
In these short notes, we will show the following. Let F_q be a finite field and let E/\F_q be an elliptic curve. Let S_r be the rth summation/Semaev polynomial for E. Under an assumption, we show that it is NP-complete to check if S_r…
In Descriptive Complexity, there is a vast amount of literature on decision problems, and their classes such as \textbf{P, NP, L and NL}. ~ However, research on the descriptive complexity of optimisation problems has been limited.…
Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large amount of information in a helpful way, but are not easy to construct, often requiring deep…
Hypersimplices are well-studied objects in combinatorics, optimization, and representation theory. For each hypersimplex, we define a new family of subpolytopes, called r-stable hypersimplices, and show that a well-known regular unimodular…