Solving State Explosion with Petri-Nets and Vector Clocks
Event driven programming has a problem formally modeling events: https://en.wikipedia.org/wiki/Event-driven_programming#Criticism
Due to the phenomenon known as "state explosion," the complexity of a traditional FSM tends to grow much faster than the complexity of the reactive system it describes. This happens because the traditional state machine formalism inflicts repetitions.
Q: What is a bitwrap machine?
A: state machine that can be used to compose a domain specific language for modeling a problem.
This stateful model (when combined with an eventstore database) provides an approachable solution for formal event driven design.
Some Computer Science:
Bitwrap converts Petri-Net Markup Language (PNML) definition to an equivilant state machine.
This state machine form is known as a Vector Addition System (with States) VASS
VASS state machine example
Given this simple 3-place Petri-Net that models a voting system:
- We can represent the state as an array of 'places'.
- Each place is acted upon by a 'transition' vector.
- We represent an instruction set as a set of deltas
- Each transition vector maps to a single instruction.
- During an execution
- Transition vectors are combined with input states using vector addition.
- Output vectors having only positive scalar integers are valid.
A 3-place Petri-Net - inital state
we execute the 'YAY' instruction
[ 1,0,0] +[-1,1,0] -------- [ 0,1,0]
once this transition happens this graph cannot execute 'YAY' again.
NOTE: Due to the properties of Petri-Nets ( representation with 'tokens') the valid range of scalar values is constrained to natural numbers. (integers >=0)
[ 0,1,0] +[-1,1,0] -------- [-1,2,0] <= invalid state
Using this machine as a programming model - we can easily validate the output of our instruction by testing for any negative scalar values.
Tic-Tac-Toe w/o State Explosion
Here we show a model for a game of Tic-Tac-Toe - which is usually difficult to create or conceptualize using other types of Deterministic state machines.
Rather than modeling every permutation of the board (as in a DFA)- the Petri-Net model describes the state of the board, and the valid actions that can be taken from a given input state.
Conclusion & Demonstration of Technique
As a programmer this type of state machine is useful in a variety of contexts.
You could use a state machine to represent a traditional workflow or task management system.
As part of the Domain Driven Design technique - PNML can be used to declare an executable specification for events declared during an Event Storming design session.
What is important is that the Petri-Nets help the author keep a clear mental picture of 'what' is being modeled.
Read our blog: http://www.blahchain.com
To understand more this approach I recommend reading a book by Eric Evans: Domain-Driven Design: Tackling Complexity in the Heart of Software