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
# Use the static class constructor to create a DFAx object
dfax = DFAx.create(
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, ReachAvoidDerived samples randomly mutated Reach and ReachAvoid DFAs, and Mixture samples from Reach, ReachAvoid, and ReachAvoidDerived with given probabilities (uniform by default).
import jax
from dfax.samplers import ReachSampler, ReachAvoidSampler, RADSampler, MixtureSampler
key = jax.random.PRNGKey(0)
sampler = ReachAvoidSampler()
dfax = sampler.sample(key)
sampler = MixtureSampler(probs=(0.5, 0.25, 0.25)) # Reach, ReachAvoid, ReachAvoidDerived
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!
1 maintainer
Metadata
1 maintainer
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