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In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
We consider the reachability problem on transition systems corresponding to succinct one-counter machines, that is, machines where the counter is incremented or decremented by a value given in binary.
We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 x 8 chessboard by a single player, with only white pieces, using…
Motivated by the real-world problem of international kidney exchange (IKEP), recent literature introduced a generalized transferable utility matching game featuring a partition of the vertex set of a graph into players, and analyzed its…
An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such an arithmetic matroid can be represented by an integer…
We point out that the computation of true \emph{proof} and \emph{disproof} numbers for proof number search in arbitrary directed acyclic graphs is NP-hard, an important theoretical result for proof number search. The proof requires a…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
The Traveling Tournament Problem (TTP-$k$) is a well-known benchmark problem in sports scheduling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, no pair of…
In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices $n=2^m$ we define the set of all the possible…
An unexpected difference between online and offline algorithms is observed. The natural greedy algorithms are shown to be worst case online optimal for Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated…
Voting is a simple mechanism to aggregate the preferences of agents. Many voting rules have been shown to be NP-hard to manipulate. However, a number of recent theoretical results suggest that this complexity may only be in the worst-case…
In this short note we consider a variation of the connectivity Waiter-Client game $WC(n,q,\mathcal{A})$ played on an $n$-vertex graph $G$ which consists of $q+1$ disjoint spanning trees. In this game in each round Waiter offers Client $q+1$…
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…
We consider the minimum-weight feedback vertex set problem in tournaments: given a tournament with non-negative vertex weights, remove a minimum-weight set of vertices that intersects all cycles. This problem is $\mathsf{NP}$-hard to solve…
The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…
The Lonely Runner Conjecture states that if $k+1$ runners start at the same point on a unit-length circular track and run with distinct constant speeds, then each runner is at some time at least $1/(k+1)$-distant from every other runner.…
In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…
We consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching…