Related papers: The Complexity of Coverage
Coverage path planning in a generic known environment is shown to be NP-hard. When the environment is unknown, it becomes more challenging as the robot is required to rely on its online map information built during coverage for planning its…
We study the maximum set coverage problem in the massively parallel model. In this setting, $m$ sets that are subsets of a universe of $n$ elements are distributed among $m$ machines. In each round, these machines can communicate with each…
Cyclic debugging requires repeatable executions. As non-deterministic or real-time systems typically do not have the potential to provide this, special methods are required. One such method is replay, a process that requires monitoring of a…
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We…
The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
The notion of compliance in Multiset Rewriting Models (MSR) has been introduced for untimed models and for models with discrete time. In this paper we revisit the notion of compliance and adapt it to fit with additional nondeterminism…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of…
This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition…
In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic external influence. This…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several…
We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the…
The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…
We analyze the computational complexity of the video game "CELESTE" and prove that solving a generalized level in it is NP-Complete. Further, we also show how, upon introducing a small change in the game mechanics (adding a new game…
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.