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Related papers: Complexity of Unambiguous Problems in $\Sigma^P_2$

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We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…

Quantum Physics · Physics 2007-11-21 Julia Kempe , Hirotada Kobayashi , Keiji Matsumoto , Ben Toner , Thomas Vidick

We know that the Nash equilibria of a game cannot be computed efficiently unless $P = PPAD$. But can they be learned? Are there dynamics that (1) can be computed efficiently by the players at each strategy profile and (2) are guaranteed to…

Computer Science and Game Theory · Computer Science 2026-04-17 Oliver Biggar , Christos Papadimitriou , Georgios Piliouras

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.…

Logic in Computer Science · Computer Science 2021-12-07 Michal Ajdarów , Antonín Kučera

The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…

Logic in Computer Science · Computer Science 2026-05-15 Maximilian Hadek , Tomáš Jakl , Jakub Opršal

The assumption that voters' preferences share some common structure is a standard way to circumvent NP-hardness results in social choice problems. While the Kemeny ranking problem is NP-hard in the general case, it is known to become easy…

Discrete Mathematics · Computer Science 2022-06-13 Bruno Escoffier , Olivier Spanjaard , Magdaléna Tydrichová

The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the…

Computer Science and Game Theory · Computer Science 2021-06-25 Zack Fitzsimmons , Edith Hemaspaandra

As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…

Data Structures and Algorithms · Computer Science 2020-11-25 Roman Galay , Daniil Kalistratov

In recent work by Johnson et al. (2022), a framework was described for the study of graph problems over classes specified by omitting each of a finite set of graphs as subgraphs. If a problem falls into the framework then its computational…

Computational Complexity · Computer Science 2025-03-17 Tala Eagling-Vose , Barnaby Martin , Daniel Paulusma , Siani Smith

Bilevel linear programs (BLPs) form a class of hierarchical decision-making problems in which both the upper-level and the lower-level decision-makers, known as the leader and the follower, respectively, solve linear optimization problems.…

Computational Complexity · Computer Science 2025-11-20 Sergey S. Ketkov , Oleg A. Prokopyev

We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…

Logic in Computer Science · Computer Science 2026-04-22 Andrei Bulatov , Xiaoyang Gong , Bakh Khoussainov , Xinyao Wang

We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and…

Logic in Computer Science · Computer Science 2009-08-04 Olivier Finkel

The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…

Computational Complexity · Computer Science 2014-07-08 Frank Vega Delgado

We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…

Computational Complexity · Computer Science 2016-09-01 Andras Farago

We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of…

Computational Complexity · Computer Science 2014-07-18 Yi Li , Xiaoming Sun , Chengu Wang , David P. Woodruff

We consider a team formation setting where agents have varying levels of expertise in a global set of required skills, and teams are ranked with respect to how well the expertise of teammates complement each other. We model this setting as…

Computer Science and Game Theory · Computer Science 2020-11-04 Bugra Caskurlu , Fatih Erdem Kizilkaya , Berkehan Ozen

We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…

Data Structures and Algorithms · Computer Science 2021-01-25 Silvia Butti , Victor Dalmau

We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…

Optimization and Control · Mathematics 2021-08-05 Christoph Buchheim , Dorothee Henke , Felix Hommelsheim

Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…

Logic in Computer Science · Computer Science 2020-09-10 Flavio Ferrarotti , Senen Gonzalez , Klaus-Dieter Schewe , Jose Maria Turull-Torres

We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted…

Formal Languages and Automata Theory · Computer Science 2025-05-28 Ismaël Jecker , Filip Mazowiecki , David Purser

We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…

Logic in Computer Science · Computer Science 2021-01-12 Pierre Gillibert , Julius Jonušas , Michael Kompatscher , Antoine Mottet , Michael Pinsker