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Holographic algorithms, alternatively known as Pfaffian circuits, have received a great deal of attention for giving polynomial-time algorithms of $\#\mathsf{P}$-hard problems. Much work has been done to determine the extent of what this…
We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position,…
Parallel operations are important for both near-term quantum computers and larger-scale fault-tolerant machines because they reduce execution time and qubit idling. We propose and implement a pairwise-parallel gate scheme on a trapped-ion…
Quadruped robots demonstrate exceptional potential for navigating complex terrain in critical applications such as search and rescue missions and infrastructure inspection However autonomous traversal of confined 3D environments including…
Building agents that can explore their environments intelligently is a challenging open problem. In this paper, we make a step towards understanding how a hierarchical design of the agent's policy can affect its exploration capabilities.…
Imagine an assembly line where a box with a lid and liquid in it enters in some unknown orientation. The box should leave the line with the open lid facing upwards with the liquid still in it. To save costs there are no complex sensors or…
A timed network consists of an arbitrary number of initially identical 1-clock timed automata, interacting via hand-shake communication. In this setting there is no unique central controller, since all automata are initially identical. We…
Polymorphic circuits are a special kind of circuits which possess some different build-in functions and these functions are activated by environment parameters, like light and VDD. Some theories have been proposed to guide the design of…
We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. In this work, we use the deployment strategy for diagonal guards…
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…
Modern AAA video games feature huge game levels and maps which are increasingly hard for level testers to cover exhaustively. As a result, games often ship with catastrophic bugs such as the player falling through the floor or being stuck…
Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity…
The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of…
We study the problem of learning a generalizable action policy for an intelligent agent to actively approach an object of interest in an indoor environment solely from its visual inputs. While scene-driven or recognition-driven visual…
We study algorithmic problems in multi-stage open shop processing systems that are centered around reachability and deadlock detection questions. We characterize safe and unsafe system states. We show that it is easy to recognize system…
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…
This paper proposes a motion control scheme for robots operating in a dynamic environment with concave obstacles. A Model Predictive Controller (MPC) is constructed to drive the robot towards a goal position while ensuring collision…
In the $15$-puzzle game, $15$ labeled square tiles are reconfigured on a $4\times 4$ board through an escort, wherein each (time) step, a single tile neighboring it may slide into it, leaving the space previously occupied by the tile as the…
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the…
This project investigates the potential of computers to solve complex tasks such as games. The paper proves that the complexity of a generalized version of spider solitaire is NP-Complete and uses much of structure of the proof that…