dfax 0.1.5

Python library for modeling DFAs, Moore Machines, and Transition Systems in JAX.

DFAx

A JAX-compatible Python implementation of a Deterministic Finite Automaton (DFA).

Installation

Install using pip.

pip install dfax

Usage

Create DFAs by specifying a start state, transitions matrix, which is max number of states by number of alphabet symbols, and the associated labels for each state.

from dfax import DFAx

dfax = DFAx(
	start=0, # State referred to as 0 is the initial state
	transitions=jnp.array([
		[1, 2, 0, 0, 0],
		[1, 1, 1, 1, 1],
		[2, 2, 2, 2, 2],
	]), # Max number of states is 3 and number of tokens is 5
	labels=jnp.array([False, True, False]) # State labels
) # Returns a DFA

Take transitions on the DFA using a given symbol.

dfax = dfax.advance(0) # Returns the resulting DFA after reading the symbol referred to as 0

Minimize DFAs.

dfax = dfax.minimize() # Returns a canonical minimal DFA

Canonicalize DFAs by relabeling states based on a BFS search.

dfax = dfax.canonicalize() # Returns a canonical DFA

Mutate DFAs by randomly toggling entries in the transition matrix.

import jax

key = jax.random.PRNGKey(0)
dfax = dfax.mutate(key) # Returns a mutated DFA

Perform syntactic equality check between DFAs.

dfax1 == dfax2

Perform semantic equality check between DFAs.

dfax1.minimize() == dfax2.minimize()

Use DFAs as reward functions. With ternary semantics, reward is (i) +1 if the start state has label True, (ii) -1 if the start state has label False and is a sink state, and (iii) 0 otherwise. With binary semantics, 0 is returned instead of -1.

dfax.reward() # Returns a ternary reward
dfax.reward(binary=True) # Returns a binary reward

Sample from different DFA distributions: Reach samples DFAs ordering alphabet symbols, ReachAvoid samples Reach DFAs but also includes Avoid constraints, and ReachAvoidDerived samples randomly mutated Reach and ReachAvoid DFAs.

import jax
from dfax.samplers import ReachSampler, ReachAvoidSampler, RADSampler

key = jax.random.PRNGKey(0)
sampler = ReachAvoidSampler()

dfax = sampler.sample(key)

Define your own DFA samplers by overloading DFASampler .

@struct.dataclass
class MySampler(DFASampler):
    @partial(jax.jit, static_argnums=(0,))
    def sample(self, key: chex.PRNGKey) -> DFAx:
        # Write sampling code and return sampled DFA

Visualize DFAs.

from dfax.utils import visualize
visualize(dfax)

This project is a JAX extension of dfa. Therefore, we include helper methods for translating DFAx objects to and from DFA objects.

from dfax import dfa2dfax, dfax2dfa

dfa = dfax2dfa(dfax) # Create DFA from DFAx
dfax = dfa2dfax(dfa) # Create DFAx from DFA

In progress

Currently, we are working on implementing Boolean operations on DFAx objects, e.g., conjunction, disjunction, etc. If there are other functionalities you would like to have in this package, create pull request or contact us to work together!