Related papers: On the Hardness of PCTL Satisfiability
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For knowledge bases in the basic description logic ALC, the computational…
The UNIQUE GAMES problem is a central problem in algorithms and complexity theory. Given an instance of UNIQUE GAMES, the STRONG UNIQUE GAMES problem asks to find the largest subset of vertices, such that the UNIQUE GAMES instance induced…
We study stochastic two-player turn-based games in which the objective of one player is to ensure several infinite-horizon total reward objectives, while the other player attempts to spoil at least one of the objectives. The games have…
We consider the model-checking problem for freeze LTL on one-counter automata (OCA). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared…
This short note aims at proving that the isolation problem is undecidable for probabilistic automata with only one probabilistic transition. This problem is known to be undecidable for general probabilistic automata, without restriction on…
We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…
Several physically inspired problems have been proven undecidable; examples are the spectral gap problem and the membership problem for quantum correlations. Most of these results rely on reductions from a handful of undecidable problems,…
Constraint LTL, a generalisation of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some real-time…
We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…
Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…
We show that the computational problem CONSENSUS-HALVING is PPA-complete, the first PPA-completeness result for a problem whose definition does not involve an explicit circuit. We also show that an approximate version of this problem is…
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 study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
We study 2-player turn-based perfect-information stochastic games with countably infinite state space. The players aim at maximizing/minimizing the probability of a given event (i.e., measurable set of infinite plays), such as reachability,…
The physics-based simulation game Angry Birds has been heavily researched by the AI community over the past five years, and has been the subject of a popular AI competition that is currently held annually as part of a leading AI conference.…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
Concurrent stochastic games are an important formalism for the rational verification of probabilistic multi-agent systems, which involves verifying whether a temporal logic property is satisfied in some or all game-theoretic equilibria of…
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 ambition constrained validity and the model witness problems in the logic UCL, for reasoning about circuits with unreliable gates, are analyzed. Moreover, two additional problems, motivated by the applications, are studied. One consists…