We present a tool [1] for the analysis of finite discrete-time Markov chains (DTMCs). As a novelty, the tool offers functional specification of DTMCs and implements forward algorithms to compute the stationary state distribution of the DTMC or derive its transition matrix . In addition, we implement nine direct and iterative algorithms to compute various metrics of DTMCs based on including an algorithm to determine the period of the DTMC.

Main window of FunSpec4DTMC [1].

The tool is intended for production purposes as well as a platform for teaching the functional specification of DTMCs.

• Status quo: analysis tools and libraries for teaching that utilize
• Gap: Library to apply the functional specification of DTMCs

For this reason FunSpec4DTMC offers the following specification types:

• Conventional Specification of DTMCs
  • States
  • Stochastic transition matrix holding transition probabilities
• Computation of consecutive state distributions
• Computation of the stationary state distribution
  • Initial state distribution
  • Consecutive state distributions

• Functional specification [2]
  • States
    • Initial state distribution
  • Factors
    • Factor distribution
  • State distribution function
    • 
    • Stochastic recursive equation
• Computation of consecutive states
• Computation of consecutive state distributions
  • Forward algorithms
    • Input:
    • Output:
      • Consecutive state distribution
        • Additional input
        • State transition matrix not needed
      • State transition matrix
• Advantages over conventional specification
  • Intuitive modelling of complex systems with a possibly multidimensional state and factor space
  • Simplified derivation of the transition matrix
  • Memory-efficient computation of consecutive state distributions

• Python 3 library published under GPLv3
  • Simulation library
  • Intuitive GUI for simplified use
• Multiple project tabs, analysis dialogues, and means for visualization
• Four phases of FunSpec4DTMC’s analysis process for DTMCs

Analysis process of FunSpec4DTMC. Taken from [1].

• Direct algorithms to calculate the stationary state distribution
• Iterative algorithms to calculate the stationary state distribution
  • DTMC random walk
    • simulation
  • Calculation of the limiting distribution
    • 
    • applicable to aperiodic DTMCs
  • Matrix powering
    • 
    • applicable to aperiodic DTMCs and to DTMCs with a period of
  • Calculation of the Cesaro limit
    • 
  • Modified calculation of the Cesaro limit [2]
    • 
    • analysis of transition structures to compute the period

• Object-oriented class hierarchy that leverages many design patterns
  • e. g.: model-view-controller, observer pattern, strategy pattern
• Minimum dependence on external libraries
  • NumPy for matrix multiplication and memory mapping
  • SciPy to use common distributions
  • Cython for runtime optimization
  • Matplotlib for figure plotting
  • NetworkX for graph visualization
  • PyQt5 for GUI programming