Related papers: LaserTank is NP-complete
In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional…
We consider two models of computation for Tarski's order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. In both models, we find the first polynomial time…
In this paper we study the computational complexity of the game of Scrabble. We prove the PSPACE-completeness of a derandomized model of the game, answering an open question of Erik Demaine and Robert Hearn.
We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it…
Given a tournament $T$, the problem MaxCT consists of finding a maximum (arc-disjoint) cycle packing of $T$. In the same way, MaxTT corresponds to the specific case where the collection of cycles are triangles (i.e. directed 3-cycles).…
Answer set programming is a well-understood and established problem-solving and knowledge representation paradigm. It has become more prominent amongst a wider audience due to its multiple applications in science and industry. The constant…
Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…
We consider the computational complexity of winning this turn (mate-in-1 or "finding lethal") in Hearthstone as well as several other single turn puzzle types introduced in the Boomsday Lab expansion. We consider three natural…
A partial Latin square of order $n$ can be represented by a $3$-dimensional chess-board of size $n\times n\times n$ with at most $n^2$ non-attacking rooks. In Latin squares, a subsystem and its most distant mate together have as many rooks…
All or Nothing, Water Walk, and Remembered Length are pencil puzzles that involve constructing a continuous loop on a rectangular grid under specific constraints. In this paper, we analyze their computational complexity using the T-metacell…
For all $k \geq 1$, we show that deciding whether a graph is $k$-planar is NP-complete, extending the well-known fact that deciding 1-planarity is NP-complete. Furthermore, we show that the gap version of this decision problem is…
We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete…
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
We consider the complexity of deciding the winner of an election under the Slater rule. In this setting we are given a tournament $T = (V, A)$, where the vertices of V represent candidates and the direction of each arc indicates which of…
In this paper, we introduce a simplicial complex representation for finite non-cooperative games in the strategic form. The covering space of the simplicial game complex is introduced and we show that the covering complex is a powerful tool…
The problem of determining whether a graph $G$ can be realized as a unit-distance graph in $\mathbb{Z}^2$ is NP-complete. As far as we can tell, a proof of this result has never been written up. We prove NP-completeness of this problem by…
It is well-known that the problem of recognizing an ESS in a symmetric bimatrix game is coNP-complete. In this paper, we show that recognizing an ESS even in doubly symmetric bimatrix games is also coNP-complete. Our result further implies…
We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse…
We formalize Simplified Boardgames language, which describes a subclass of arbitrary board games. The language structure is based on the regular expressions, which makes the rules easily machine-processable while keeping the rules concise…
After examining the {\bf P} versus {\bf NP} problem against the Kleene-Rosser paradox of the $\lambda$-calculus [94], it was found that it represents a counter-example to NP-completeness. We prove that it contradicts the proof of Cook's…