Inspirations:

• OpenFST
• Ken Thompson's NFA algorithm

FSMs are effectively directed graphs (with a global source), so I extracted everything possible into a directed graph class.

https://github.com/automatthew/djinn/blob/master/src/digraph.coffee

The FSA class extends Digraph. It has accept, match, and matches methods for testing input strings or arrays. It's still suffering from cruft, feature creep, and indecision. The test script shows you pretty much all the primitives it offers.

https://github.com/automatthew/djinn/blob/master/src/fsa.coffee https://github.com/automatthew/djinn/blob/master/test/fsaTest.js

I had graphs on the brain this weekend, so I refurbished Djinn.

There's now a base Digraph class that requires you to implement your own Vertex and Arc (a.k.a. node and edge) classes. So far I supply a NaiveDigraph subclass that's based on mindless OO patterns and a SequenceAcceptor (currently using NaiveDigraph, but could use any other Digraph class). The SequenceAcceptor is a limited FSM for matching strings or arrays.

Aside from refurbishings, the really cool thing that happened was the implementation of digraph-intersection. In other words, Djinn can now take two FSMs and generate an intersection of the grammars they express. String matching is a special case of FSA intersection where the string is assumed to be a trivial FSA with each state having one and only one transition to the next state.

Near Future Coolness: the intersection algorithm for finite state acceptors is apparently a special case of the composition algorithm for finite state transducers. That is, where an Acceptor can only return matches from inputs, a Transducer can return transformations. FSTransducer composition is exactly analogous to function or set composition.

Limitations: I stepped waaaay back from my idea of allowing each FSA transition to do arbitrary matching. Doing anything other than exact matching drops you straight into Cartesian Product territory. That territory may well be worth exploring for situations with known bounds on the number of arcs per vertex (aka transitions leaving each state), but I'm not assuming that constraint for now. It should be near-trivial to add later, by augmenting the way the Arc classes test equivalence.

Interoperability: AT&T's fsm and OpenFST emit and consume simple text formats. Djinn easily could be modified to emit/consume these formats. This means that a production environment could take FSMs created in the browser by Djinn and perform complex, CPU intensive operations with a highly-optimized OpenFST application. Or a browser could use Djinn to perform less intensive operations on an FSM constructed and maintained by OpenFST.

TODOS:

• subclass of Digraph that uses an adjacency list for vertex/arc operations
• dump/load functions for OpenFST text format
• transducer subclass (both input and output values for each arc)
• regex compiler (mostly for demo)
• subclass that maintains a codebook of arc values, using integer labels for the actual arc storage.