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Combinatorial games played between two players, called Spoiler and Duplicator, have often been used to capture syntactic properties of formal logical languages. For instance, the widely used Ehrenfeucht-Fra\"iss\'e (EF) game captures the…

Logic in Computer Science · Computer Science 2025-08-01 Ronald Fagin , Neil Immerman , Phokion Kolaitis , Jonathan Lenchner , Rik Sengupta

Exact tight bounds of the complexity of the satisfiability problem for dense modal logics is a difficult question, likely somewhere between $\PSPACE$ and $\EXPSPACE$ depending of the logic under question. For a class of them, called here…

Logic in Computer Science · Computer Science 2026-04-21 Olivier Gasquet

We note that the remarkable EXPSPACE-hardness result in [G\"oller, Haase, Ouaknine, Worrell, ICALP 2010] ([GHOW10] for short) allows us to answer an open complexity question for simulation preorder of succinct one counter nets (i.e., one…

Logic in Computer Science · Computer Science 2018-01-04 Petr Jancar , Petr Osicka , Zdenek Sawa

We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…

Computer Science and Game Theory · Computer Science 2022-04-26 Léonard Brice , Jean-François Raskin , Marie van den Bogaard

We show that the widely used homotopy method for solving fixpoint problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we…

Computer Science and Game Theory · Computer Science 2011-08-05 Paul W. Goldberg , Christos H. Papadimitriou , Rahul Savani

We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (LMCS 2016) for simulation preorder on the class of succinct one-counter nets (i.e., one-counter automata with no zero tests where counter increments and decrements are…

Logic in Computer Science · Computer Science 2023-06-22 Petr Jancar , Petr Osicka , Zdenek Sawa

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…

In a recently launched research program for developing logic as a formal theory of (interactive) computability, several very interesting logics have been introduced and axiomatized. These fragments of the larger Computability Logic aim not…

Logic in Computer Science · Computer Science 2013-04-02 Matthew S. Bauer

It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators,…

Computational Complexity · Computer Science 2008-12-18 Edith Hemaspaandra , Henning Schnoor , Ilka Schnoor

Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…

Logic in Computer Science · Computer Science 2014-05-01 Amir M. Ben-Amram , Michael Vainer

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

Computer Science and Game Theory · Computer Science 2008-03-05 Josep Freixas , Xavier Molinero , Martin Olsen , Maria Serna

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated…

Computer Science and Game Theory · Computer Science 2015-02-06 Felix Brandt , Felix Fischer , Markus Holzer

Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…

Computational Complexity · Computer Science 2026-02-16 Christoph Grüne , Berit Johannes , James B. Orlin , Lasse Wulf

We study the computational complexity of distance games, a class of combinatorial games played on graphs. A move consists of colouring an uncoloured vertex subject to it not being at certain distances determined by two sets, D and S. D is…

Computational Complexity · Computer Science 2019-02-12 Kyle Burke , Silvia Heubach , Melissa Huggan , Svenja Huntemann

Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the…

Logic in Computer Science · Computer Science 2007-05-23 Edith Hemaspaandra

We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…

Discrete Mathematics · Computer Science 2026-04-14 Florian Galliot

This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and…

Optimization and Control · Mathematics 2021-12-22 Eugene A. Feinberg , Pavlo O. Kasyanov , Michael Z. Zgurovsky

It is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present…

Data Structures and Algorithms · Computer Science 2007-05-23 Volker Diekert , Claudio Gutierrez , Christian Hagenah

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…

Computational Complexity · Computer Science 2022-04-01 Jeffrey Bosboom , Josh Brunner , Michael Coulombe , Erik D. Demaine , Dylan H. Hendrickson , Jayson Lynch , Elle Najt

The reversible pebble game is a combinatorial game played on rooted DAGs. This game was introduced by Bennett (1989) motivated by applications in designing space efficient reversible algorithms. Recently, Chan (2013) showed that the…

Computational Complexity · Computer Science 2016-04-20 Balagopal Komarath , Jayalal Sarma , Saurabh Sawlani