Project 2: Non-Lanchester theory battle simulation (100 points) Much effort, time and money are spent doing combat simulations. The interest is not just academic, the desire to win battles is approached by the desire to preserve resources such as equipment and most importantly human lives. During 1916 Frederick Lanchester came up with a set of differential equations to show the power relationships between opposing forces. You can read about his Linear Law (for ancient combat) and his Square Law (for modern combat) in this wikipedia entry: https://en.wikipedia.org/wiki/Lanchester%27s_laws. These equations form a fundamental part of modern combat theory. There have been efforts to validate these equations using historical data and there has been some success, specifically the battle of Gettysburg [Sodergren 2015] and the Battle of Britain [MacKay 2011]. However, while in graduate school I took a course in Strategic Arms Limitation and Combat Simulations. I was required to read a paper by a professor at the Brookings Institute named Joshua M. Epstein, It is entitled "THE CALCULUS OF CONVENTIONAL WAR: DYNAMIC ANALYSIS WITHOUT LANCHESTER THEORY" . While it is now part of a book published by the Department of Defense, [Studies in Defense Policy], I want to thank Professor Epstein who sent me the pdf and gave me permission to make it available as part of my class assignments to you directly. Please do not distribute outside of this course. You may download a copy of the pdf at http://www.cs.odu.edu\~cs355m\Papers\warfare_calculus.pdf Your assignment is to reproduce the results obtained by Professor Epstein in his paper using software written in PROLOG. You will find the paper to be rather well written and self-explanatory but basically, this is a time stepping solution that uses algebraic equations to simulate two forces, red and blue, they have ground and air lethalities. The idea is that the defender will trade land for lives, the attacker will expend its forces to take the ground, losses are computed at each day and applied. Ground to Ground, Air to Ground, and Air to Air components are taken into account GRADING: Incomplete but substantial working code: 70 to 79 depending upon the amount of working code submitted. Successful completion of the basic model. 80 to 93 depending upon how many of Epstiens results you can replicate. In addition, you may add as many of the following OPTIONS as you like to your code. Each of them is worth 10 points. A. Implementation of n vs. n combat model by expanding the 1 vs. 1 model provided B. Implementation of n types of ground forces instead of infantry and armor. Specifically tank type 1, tank 2 etc..each with unique lethalities. C. Implementation of n types of air forces instead of just air-ground and air-air Additional notes: Option A: imagine that there are multiple armies, with individual lethal capabilities. For example 3 red vs. 2 blue. You must provide some "geographical setting:", e.g. Red1 vs. Blue1 and Red2 vs. Blue 2 and with Red 3 being allowed to move from battle to battle as needed. You have the authority to create the setting as you see fit. Option B and C. Both of these will require you to create a lethality matrix that shows the effectiveness of each different type of weapon for one army vs the other. For example Red_tank_1 vs. Blue_tank_1 has lethality X, but Red_tank_1 vs. Blue_Tank_2 has lethality 2X. All possible combinations must be accounted for and you must provide some scheme that allocates forces in a reasonable manner.