Related papers: Tight Upper Bounds for Streett and Parity Compleme…

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…

We revisit the classic Maximum $k$-Coverage problem: Determine the largest number $t$ of elements that can be covered by choosing $k$ sets from a given family $\mathcal{F} = \{S_1,\dots, S_n\}$ of a size-$u$ universe. A notable special case…

We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…

Simon's problem is one of the most important problems demonstrating the power of quantum computers, which achieves a large separation between quantum and classical query complexities. However, Simon's discussion on his problem was limited…

We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…

Complementation of B\"uchi automata is an essential technique used in some approaches for termination analysis of programs. The long search for an optimal complementation construction climaxed with the work of Schewe, who proposed a…

We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…

We demonstrate that any $\Pi_\alpha$ sentence of the infinitary logic $L_{\omega_1 \omega}$ extending the theory of linear orderings has a model with a $\Pi_{\alpha+4}$ Scott sentence and hence of Scott rank at most $\alpha+3$. In other…

Let $\zeta$ be a real transcendental number. We introduce a new method to find upper bounds for the classical exponent $\widehat{w}_{n}(\zeta)$ concerning uniform polynomial approximation. Our method is based on the parametric geometry of…

We resolve an open question by determining matching (asymptotic) upper and lower bounds on the state complexity of the operation that sends a language L to (c(L*))*, where c() denotes complement.

The All-Pairs Max-Flow problem has gained significant popularity in the last two decades, and many results are known regarding its fine-grained complexity. Despite this, wide gaps remain in our understanding of the time complexity for…

A tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word. The height of the tower is the number of words in the sequence. If there is no infinite tower (a tower of…

We give a lower bound of $\Omega(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\{0,1\}^n$ whose value…

An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…

We improve Luczak's upper bounds on the length of the longest cycle in the random graph G(n,M) in the "supercritical phase" where M=n/2+s and s=o(n) but n^{2/3}=o(s). The new upper bound is (6.958+o(1))s^2/n with probability 1-o(1) as n…

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…

The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong…

We study the problem of estimating the size of maximum matching and minimum vertex cover in sublinear time. Denoting the number of vertices by $n$ and the average degree in the graph by $\bar{d}$, we obtain the following results for both…

We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…

We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have…