Related papers: Bounded degree QBF and positional games
We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…
We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…
As a natural variant of the $k$-SAT problem, NAE-$k$-SAT additionally requires the literals in each clause to take not-all-equal (NAE) truth values. In this paper, we study the worst-case time complexities of solving NAE-$k$-SAT and…
We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of…
We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…
Bonnet et al. (FOCS 2020) introduced the graph invariant twin-width and showed that many NP-hard problems are tractable for graphs of bounded twin-width, generalizing similar results for other width measures, including treewidth and…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
We show that for every fixed $k\geq 3$, the problem whether the termination/counter complexity of a given demonic VASS is $\mathcal{O}(n^k)$, $\Omega(n^{k})$, and $\Theta(n^{k})$ is coNP-complete, NP-complete, and DP-complete, respectively.…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…
In this paper, we study two-player zero-sum turn-based games played on a finite multidimensional weighted graph. In recent papers all dimensions use the same measure, whereas here we allow to combine different measures. Such heterogeneous…
We exhibit families of $4$-CNF formulas over $n$ variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) $d$ but require SOS proofs of size $n^{\Omega(d)}$ for values of $d = d(n)$ from constant all the…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
This paper addresses the quantitative verification of finite-time constrained occupation time for stochastic continuous-time systems governed by stochastic differential equations (SDEs). Unlike classical reachability analysis, which focuses…
We consider the computational complexity of pure Nash equilibria in graphical games. It is known that the problem is NP-complete in general, but tractable (i.e., in P) for special classes of graphs such as those with bounded treewidth. It…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBFs) such that a game instance admits a winning…
We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the…