Related papers: PSPACE-Completeness of Reversible Deterministic Sy…
We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…
We introduce the first complete formal solution to corrigibility in the off-switch game, with provable guarantees in multi-step, partially observed environments. Our framework consists of five *structurally separate* utility heads --…
It is well known that Sokoban is PSPACE-complete (Culberson 1998) and several of its variants are NP-hard (Demaine et al. 2003). In this paper we prove the NP-hardness of some variants of Sokoban where the warehouse keeper can only pull…
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…
Amazons is a board game which combines elements of Chess and Go. It has become popular in recent years, and has served as a useful platform for both game-theoretic study and AI games research. Buro showed that simple Amazons endgames are…
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 consider finite-horizon and infinite-horizon versions of a dynamic game with $N$ selfish players who observe their types privately and take actions that are publicly observed. Players' types evolve as conditionally independent Markov…
Windows have been introduce in \cite{BalGasq25} as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the ``folklore'' case of bimodal $\K4$ already treated…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of…
Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG…
Tumbleweed is a popular two-player perfect-information new territorial game played at the prestigious Mind Sport Olympiad. We define a generalized version of the game, where the board size is arbitrary and so is the possible number of…
Games are natural models for multi-agent machine learning settings, such as generative adversarial networks (GANs). The desirable outcomes from algorithmic interactions in these games are encoded as game theoretic equilibrium concepts, e.g.…
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…
We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using elementary transformations, while…
This paper develops a Multiset Rewriting language with explicit time for the specification and analysis of Time-Sensitive Distributed Systems (TSDS). Goals are often specified using explicit time constraints. A good trace is an infinite…
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…
Analyzing refutations of the well known 0pebbling formulas Peb$(G)$ we prove some new strong connections between pebble games and algebraic proof system, showing that there is a parallelism between the reversible, black and black-white…
We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata…