Related papers: Limits of Rush Hour Logic Complexity
Consider $n^2-1$ unit-square blocks in an $n \times n$ square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable -- a variation of Rush Hour with only $1 \times 1$ cars and fixed…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
Models of parking in which cars are placed randomly and then move according to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff introduced a model…
Algorithmic reasoning is a fundamental cognitive ability that plays a pivotal role in problem-solving and decision-making processes. Reinforcement Learning (RL) has demonstrated remarkable proficiency in tasks such as motor control,…
Large Reasoning Models (LRMs) have demonstrated impressive performance on complex tasks, including logical puzzle games that require deriving solutions satisfying all constraints. However, whether they can flexibly apply appropriate rules…
Traffic forecasting plays a key role in Intelligent Transportation Systems, and significant strides have been made in this field. However, most existing methods can only predict up to four hours in the future, which doesn't quite meet…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
Large language models (LLMs) excel at many supervised tasks but often struggle with structured reasoning in unfamiliar settings. This discrepancy suggests that standard fine-tuning pipelines may instill narrow, domain-specific heuristics…
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Rush hour and sustained traffic flows in eight cities are studied using the IBM Mega Traffic Simulator to understand the importance of road structures and vehicle acceleration in the prevention of gridlock. Individual cars among the tens of…
The goal of this paper is to propose and test a new memetic algorithm for the capacitated vehicle routing problem in parallel computing environment. In this paper we consider simple variation of vehicle routing problem in which the only…
Two multivehicle routing problems are considered in the framework that a visit to a location must take place during a specific time window in order to be counted and all time windows are the same length. In the first problem, the goal is to…
As an example of the concept of rulial space, we explore the case of simple Turing machines. We construct the rulial multiway graph which represents the behavior of all possible Turing machines with a certain class of rules. This graph…
We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…
We study the problem of planning routes in road networks when certain streets or areas are closed at certain times. For heavy vehicles, such areas may be very large since many European countries impose temporary driving bans during the…
We present PLUGH (https://www.urbandictionary.com/define.php?term=plugh), a modern benchmark that currently consists of 5 tasks, each with 125 input texts extracted from 48 different games and representing 61 different (non-isomorphic)…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
The success of language models has inspired the NLP community to attend to tasks that require implicit and complex reasoning, relying on human-like commonsense mechanisms. While such vertical thinking tasks have been relatively popular,…