FranceLab 1 - Kordel K. France

This project was constructed for the Foundations of Algorithms class, 605.621 section 83, at Johns Hopkins University.

The project illustrates the definition, construction, and asymptotic costs of different Deterministic Turing Machines (DTMs). The file DTM_handler.py contains the construction of all four required DTMs. There is one DTM for each of the following: a) a pattern recognition DTM leveraged from the class notes called "DEMO" that detects a pattern of multiple zeros in binary strings (see build_dtm_demo), b) an addition DTM that adds two binary strings (see build_dtm_add), c) a subtractive DTM that subtracts one binary string from the other (see build_dtm_sub), and d) a multiplicative DTM that multiplies two binary strings together (see build_mul_dtm).

IMPORTANT: Please note that when n is mentioned, it refers to the length of a binary string, such that 10 represents a binary string of n=2, and 1001 represents a binary string of n=4. Obviously larger values of n will result in more algorithmic operations by the DTM, so this was the metric scaled to determine the associated runtime complexities for each DTM.

Running FranceLab1

1. Ensure Python 3.7 is installed on your computer.
2. Navigate to the Lab0 directory. For example, cd User\Documents\PythonProjects\FranceLab1. Do NOT cd into the Lab1 module.
3. Run the program as a module: python -m Lab1.
4. Input and output files ar located in the io_files subdirectory. In here, here are input and output folders containing files of the same type. In the input, the input required from class is inside files with reqInput in the name and the names are formatted as traceRun_{DTM_TYPE}_correctness_reqInput.txt where DTM_TYPE is the type of DTM used count.

Note: When the module is run, traceRuns will automatically regenerate for different counts of n. These files are coded as traceRun_{DTM_TYPE}_{RUN_TYPE}_n{n} where DTM_TYPE is the specific DTM used for the run, RUN_TYPE specifies either cost or correctness run, and n specifies the number of digits in each binary operand for that run. You will see traceRuns for n = 100 in the io_files directory but these are provided for reference and will not regenerate at runtime due to the time it takes to complete these trace runs.

Lab1 Usage

usage: python -m Lab1

Note that the project takes about 3 minutes to fully execute since time delays are incorporated to easier visualize execution of the DTM.

Project Layout

Here is how the project is structured and organized.

• FranceLab1: The parent folder of the project. This should be the last subdirectory you navigate to to run the project.
  • README.md: A guide on what the project does, how to run the project, etc.
  • io_files: A subdirectory containing all of the input and output .txt files.
  • Lab1: This is the module of the entire program package. It is not a directory. Do not navigate into it.
    • __init__.py As the name suggests, this file initializes the program and gives access to the file processing capabilities to other programs.
    • __main__.py This file processes the I/O files, begins the general program, generates trace runs, and facilitates the presentation of the final graph.
    • DTM.py This file establishes a class for a Deterministic Turing Machine and its functionality.
    • DTM_handler.py This file contains handlers to build and run DTM algorithms. It facilitates the construction and operation of each DTM.
    • Rule.py This file establishes a class for an object called Rule, which is a logic argument for a DTM.
    • Tape.py This file establishes a class for a set of inputs called Tape that is read by a DTM and gives it directions.
    • config.py This file contains hyperparameters to control debugging features.
    • file_processing.py This file contains I/O methods for processing the input and output .txt files contained in the io_files directory.
    • helpers.py This file contains helper methods for common utilities used throughout the app, including cost counters.
    • graph.py This file contains a function to graph and display algorithmic efficiency data.

###References The following items were used as references for the construction of this project.

1. Miller, B. N., & Ranum, D. L. (2014). Problem solving with algorithms and data structures using Python (2nd ed.). Decorah, IA: Brad Miller, David Ranum.
2. Cormen, T. H., & Leiserson, C. E. (2009). Introduction to Algorithms, 3rd edition.
3. Kleinberg, John & Tardos, Eva. (2014). Algorithm Design. Dorling Kindersley.