如何在内部表示确定性有限自动机

Question

I have a big Deterministic Finite Automaton with ~15M states and the current Java implementation is rather slow and memory-consuming. I am looking for a compact and fast representation that could replace the current code.

The automaton consists of the following parts:

1. States identified by integers. The initial state is always state 0 .
2. State transitions (triple of source state id, character for transition or wildcard (max 32 values), target state id).
3. A Set of accepting states.

I am experimenting with the following approaches, and I am looking for other ideas.

1. Using Java Collections

The state transitions are represented in the following way:

final List<Map<Character, Integer>> transitions = new ArrayList<>();
final Set<Integer> acceptingStates = new HashSet<>();

The i'th item in the list contains the state transitions for the i'th state. Some profiling shown me that most of the execution time is taken my accessing the map.

2. Arrays of arrays

final int[][] states = new int[STATE_COUNT][32];
Set<Integer> acceptingStates = new HashSet<>();

The i'th row contains state transitions for the i'th state. The j'th column of the inner array contains the id of the state for the j'th character from i'th state or -1 when missing.

This representation is much faster, but it still takes up least N * 32 * 4 bytes.

Answer 1

I would propose a framework to implement your state machine but one statement in your definition puzzles me, you have 15M States or 15M State Machine instances.

If your application is a Server Side application that can cluster up to host 15M State Machine instances or 15M States, I would propose that you look to the Akka Finite State Machine framework.

Akka Framework has a very low memory footprint for State Machine instances, which can satisfy your requirement. I personally developed systems with 50M State Machine instances and the system could easily contain much more then that.

If you need an implementation example, you can check my following blogs blog1 blog2 .

I hope this would help you.