Related papers: Walking through Doors is Hard, even without Stairc…
We prove PSPACE-completeness of two classic types of Chess problems when generalized to n-by-n boards. A "retrograde" problem asks whether it is possible for a position to be reached from a natural starting position, i.e., whether the…
MAPF problem aims to find plans for multiple agents in an environment within a given time, such that the agents do not collide with each other or obstacles. Motivated by the execution and monitoring of these plans, we study Dynamic MAPF…
The Internet has become a critical communication infrastructure for citizens to organize protests and express dissatisfaction with their governments. This fact has not gone unnoticed, with governments clamping down on this medium via…
Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative…
Dynamic networks of concurrent pushdown systems (DCPS) are a theoretical model for multi-threaded recursive programs with shared global state and dynamical creation of threads. The (global) state reachability problem for DCPS is undecidable…
Reachability problems in infinite-state systems are often subject to extremely high complexity. This motivates the investigation of efficient overapproximations, where we add transitions to obtain a system in which reachability can be…
The Generalized Sliding-Tile Puzzle (GSTP), allowing many square tiles on a board to move in parallel while enforcing natural geometric collision constraints on the movement of neighboring tiles, provide a high-fidelity mathematical model…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
The world is filled with articulated objects that are difficult to determine how to use from vision alone, e.g., a door might open inwards or outwards. Humans handle these objects with strategic trial-and-error: first pushing a door then…
The emerging ``Floor plan from human trails (PfH)" technique has great potential for improving indoor robot navigation by predicting the traversability of occluded floors. This study presents an innovative approach that replaces…
There are a number of results saying that for certain "path-following" algorithms that solve PPAD-complete problems, the solution obtained by the algorithm is PSPACE-complete to compute. We conjecture that these results are special cases of…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such a robot has never been achieved, although this is widely…
A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown store. A PVASS is said to be \emph{bidirected} if every transition (pushing/popping a symbol or modifying a counter) has an…
The Transience objective is not to visit any state infinitely often. While this is not possible in finite Markov Decision Process (MDP), it can be satisfied in countably infinite ones, e.g., if the transition graph is acyclic. We prove the…
Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in…
This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier…
Locomotion for legged robots poses considerable challenges when confronted by obstacles and adverse environments. Footstep planners are typically only designed for one mode of locomotion, but traversing unfavorable environments may require…
Let each site of the square lattice $\mathbb{Z}^2$ be independently assigned one of three states: a \textit{trap} with probability $p$, a \textit{target} with probability $q$, and \textit{open} with probability $1-p-q$, where $0<p+q<1$.…
Robust humanoid stair climbing remains challenging due to geometric discontinuities, sensitivity to step height variations, and perception uncertainty in real-world environments. Existing learning-based locomotion policies often rely on…