Related papers: Spider Solitaire is NP-Complete

We investigate the parameterized complexity of several problems formalizing cluster identification in graphs. In other words we ask whether a graph contains a large enough and sufficiently connected subgraph. We study here three relaxations…

Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…

We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an…

The computational characterization of game-theoretic solution concepts is a central topic in artificial intelligence, with the aim of developing computationally efficient tools for finding optimal ways to behave in strategic interactions.…

Many of the famous single-player games, commonly called puzzles, can be shown to be NP-Complete. Indeed, this class of complexity contains hundreds of puzzles, since people particularly appreciate completing an intractable puzzle, such as…

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…

The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can…

For an NP intersect coNP function g of the Nisan-Wigderson type and a string b outside its range we consider a two player game on a common input a to the function. One player, a computationally limited Student, tries to find a bit of g(a)…

We prove that for every $d\geq 2$, deciding if a pure, $d$-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for…

A 3-SAT problem is called positive and planar if all the literals are positive and the clause-variable incidence graph (i.e., SAT graph) is planar. The NAE 3-SAT and 1-in-3-SAT are two variants of 3-SAT that remain NP-complete even when…

The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…

We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…

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…

We analyze some of the many game mechanics available to Link in the classic Legend of Zelda series of video games. In each case, we prove that the generalized game with that mechanic is polynomial, NP-complete, NP-hard and in PSPACE, or…

We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing…

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

Building on the results published in arxiv:2004.12849 we present a general framework for demonstrating the NP-hardness of satisfying many genres of loop and path puzzles using a 'T-metacell' gadget. We then use this to prove the…

Maximum 2-satisfiability (MAX-2-SAT) is a type of combinatorial decision problem that is known to be NP-hard. In this paper, we compare LightSolver's quantum-inspired algorithm to a leading deep-learning solver for the MAX-2-SAT problem.…

We study the computational complexity of decision problems about Nash equilibria in $m$-player games. Several such problems have recently been shown to be computationally equivalent to the decision problem for the existential theory of the…