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We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…

Artificial Intelligence · Computer Science 2007-05-23 M. L. Littman , J. Goldsmith , M. Mundhenk

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…

Computational Complexity · Computer Science 2017-01-09 Hubie Chen , Benoit Larose

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…

Computational Complexity · Computer Science 2022-03-16 Marco Sälzer , Martin Lange

This study examines the computational complexity of the decision problem modeled on the smartphone game Bus Out. The objective of the game is to load all the passengers in a queue onto appropriate buses using a limited number of bus parking…

Computational Complexity · Computer Science 2025-05-15 Takehiro Ishibashi , Ryo Yoshinaka , Ayumi Shinohara

The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and…

Category Theory · Mathematics 2022-11-04 Soichiro Fujii , Yuni Iwamasa , Kei Kimura

We close the gap in the proof (published by Chen and Lin) of formulas for the minimum number of questions required in the expected case for Mastermind and its variant called AB game, where both games are played with two pegs and $n$ colors.…

Combinatorics · Mathematics 2018-08-14 Marcin Peczarski

We study variants of Mastermind, a popular board game in which the objective is sequence reconstruction. In this two-player game, the so-called \textit{codemaker} constructs a hidden sequence $H = (h_1, h_2, \ldots, h_n)$ of colors selected…

Combinatorics · Mathematics 2017-09-27 Aaron Berger , Christopher Chute , Matthew Stone

In connection with machine arithmetic, we are interested in systems of constraints of the form x + k \leq y + k'. Over integers, the satisfiability problem for such systems is polynomial time. The problem becomes NP complete if we restrict…

Computational Complexity · Computer Science 2008-11-07 Nikolaj Bjørner , Andreas Blass , Yuri Gurevich , Madan Musuvathi

Previously, all known variants of the Quantum Satisfiability (QSAT) problem, i.e. deciding whether a $k$-local ($k$-body) Hamiltonian is frustration-free, could be classified as being either in $\mathsf{P}$; or complete for $\mathsf{NP}$,…

Quantum Physics · Physics 2025-06-10 Ricardo Rivera Cardoso , Alex Meiburg , Daniel Nagaj

A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…

Logic in Computer Science · Computer Science 2022-04-01 Michael Pinsker

Despite its long history, the classical game of peg solitaire continues to attract the attention of the scientific community. In this paper, we consider two problems with an algorithmic flavour which are related with this game, namely…

Discrete Mathematics · Computer Science 2016-05-16 Luciano Gualà , Stefano Leucci , Emanuele Natale , Roberto Tauraso

The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…

Computational Complexity · Computer Science 2008-09-07 Jerrald Meek

We give a simple proof of that determining solvability of Shisen-Sho boards is NP-complete. Furthermore, we show that under realistic assumptions, one can compute in logarithmic time if two tiles form a playable pair. We combine an…

Data Structures and Algorithms · Computer Science 2020-10-20 Michiel de Bondt

The k-satisfiability problem is a well-known task in computational complexity theory. In this paper approach for it's solving is introduced.

Computational Complexity · Computer Science 2012-06-01 Sergey Kardash

Fortification-interdiction games are tri-level adversarial games where two opponents act in succession to protect, disrupt and simply use an infrastructure for a specific purpose. Many such games have been formulated and tackled in the…

Computational Complexity · Computer Science 2025-12-22 Alberto Boggio Tomasaz , Margarida Carvalho , Roberto Cordone , Pierre Hosteins

We analyze the computational complexity of the video game "CELESTE" and prove that solving a generalized level in it is NP-Complete. Further, we also show how, upon introducing a small change in the game mechanics (adding a new game…

Computational Complexity · Computer Science 2022-12-02 Zeeshan Ahmed , Alapan Chaudhuri , Kunwar Shaanjeet Singh Grover , Ashwin Rao , Kushagra Garg , Pulak Malhotra

Zeiger is a pencil puzzle consisting of a rectangular grid, with each cell having an arrow pointing in horizontal or vertical direction. Some cells also contain a positive integer. The objective of this puzzle is to fill a positive integer…

Computational Complexity · Computer Science 2025-03-04 Suthee Ruangwises

0-1 Knapsack is a fundamental NP-complete problem. In this article we prove that it remains NP-complete even when the weights of the objects in the packing constraints and their values in the objective function satisfy specific stringent…

Computational Complexity · Computer Science 2009-10-15 Chinmay Karande

For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…

Statistical Mechanics · Physics 2007-05-23 Henri Orland , Michel Bauer

I consider the natural infinitary variations of the games Wordle and Mastermind, as well as their game-theoretic variations Absurdle and Madstermind, considering these games with infinitely long words and infinite color sequences and…

Logic · Mathematics 2023-09-06 Joel David Hamkins