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Physical Sciences and Mathematics Commons™

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Theory and Algorithms

University of Minnesota Morris Digital Well

Journal

2022

Articles 1 - 6 of 6

Full-Text Articles in Physical Sciences and Mathematics

Intuitr: A Theorem Prover For Intuitionistic Propositional Logic, Erik Rauer Jul 2022

Intuitr: A Theorem Prover For Intuitionistic Propositional Logic, Erik Rauer

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

A constructive proof proves the existence of a mathematical object by giving the steps necessary to construct said object. Proofs of this type can be interpreted as an algorithm for creating such an object. Intuitionistic Propositional Logic (IPL) is a propositional logic system wherein all valid proofs are constructive. intuitR is a theorem prover for IPL, that is, it determines whether a given formula is valid in IPL or not. In this paper, we describe how intuitR determines the validity of a formula and review its performance. When compared on a benchmark set of problems, intuitR was determined to solve …

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Filling Gaps On The Pareto Front In Multi- And Many-Objective Optimization, Richard Lussier Jul 2022

Filling Gaps On The Pareto Front In Multi- And Many-Objective Optimization, Richard Lussier

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

Pareto fronts offer insight into the best found solutions of a given problem. Several algorithms have been developed to help maintain a well-distributed Pareto front and therefore offer a wide variety of solutions. However, in real-world problems, the Pareto front isn’t necessarily a continuous surface and may contain holes and/or discontinuous lines. These irregular areas on the Pareto front are considered gaps. These gaps can either be natural or artificial. In their research, Pellicer, Escudero, Alzueta, and Deb suggest a three-step procedure to find, validate, and fill these gaps. First, they developed an algorithm to generate gap points. Second, they …

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Using Temporal Session Types To Analyze Time Complexities Of Concurrent Programs, Joseph M. Walbran Mar 2022

Using Temporal Session Types To Analyze Time Complexities Of Concurrent Programs, Joseph M. Walbran

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

Das et al. develop a method for analyzing the time complexity of concurrent, message-passing algorithms. Their method is based on adding timing information to datatypes. Specifically, they use a family of datatypes called session types; these constrain the structure of interactions that may take place over a channel of communication. In Das’s system, the timing properties of an algorithm can be verified by a typechecker: if the timing information in the session types is mismatched, the computer will report a type error. In their paper, Das et al. develop the theory for such a typechecker, but do not provide an …

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The Impact Of Dynamic Difficulty Adjustment On Player Experience In Video Games, Chineng Vang Mar 2022

The Impact Of Dynamic Difficulty Adjustment On Player Experience In Video Games, Chineng Vang

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

Dynamic Difficulty Adjustment (DDA) is a process by which a video game adjusts its level of challenge to match a player’s skill level. Its popularity in the video game industry continues to grow as it has the ability to keep players continuously engaged in a game, a concept referred to as Flow. However, the influence of DDA on games has received mixed responses, specifically that it can enhance player experience as well as hinder it. This paper explores DDA through the Monte Carlo Tree Search algorithm and Reinforcement Learning, gathering feedback from players seeking to understand what about DDA is …

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Scheduling Aircraft Departures To Avoid Enroute Congestion, Johannes Martinez Mar 2022

Scheduling Aircraft Departures To Avoid Enroute Congestion, Johannes Martinez

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

When scheduled flights are forecast to overcrowd sections of enroute airspace, an air traffic control authority may need to delay departures. Mixed integer linear programming can be used to compute a schedule that resolves the congestion while bringing the sum of all delays to a minimum. Standard linear programming constraint formulations for such scheduling problems, however, have poor run times for instances of realistic size. A new constraint formulation based on cycles and paths through a route graph reduces run times in computational experiments. It shows particularly strong performance for schedules that approach the worst-case solution times in standard formulations.

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Fighting Gerrymandering By Automating Congressional Redistricting, Jacob Jenness Mar 2022

Fighting Gerrymandering By Automating Congressional Redistricting, Jacob Jenness

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

Gerrymandering is a political problem that the United States has had for more than 200 years. Politicians have taken the dull and routine process of drawing congressional districts and turned it into a highly-partisan process. However, with recent improvements in redistricting algorithms, researchers Harry Levin and Sorelle Friedler have introduced their recursive Divide and Conquer Redistricting Algorithm. This algorithm has the potential to automate the process of congressional redistricting, thereby removing the potential for bias. By utilizing a set of partitioning and swapping algorithms, the Divide and Conquer Redistricting Algorithm achieves desirable goals, such as low population deviation, and high …

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