morphata 1.0.2

Flexible automata representations for regular and ω-regular languages.

Morphata

Morphata is a Python library for constructing, manipulating, and translating automata over regular and omega-regular languages. It provides flexible graph-based representations for automata without committing to any specific model checking or monitoring algorithm.

Features

• Graph-based automata implementations

  • Nondeterministic Finite Automata (NFA) for finite words
  • STREL automata for spatio-temporal specifications

• HOA format parser

  • Extended HOA v1 format with finite-word acceptance support
  • Standard acceptance conditions: Buchi, co-Buchi, Rabin, Streett, Parity, Muller
  • Extension: Final(n) operator for finite-word automata (not in standard HOA v1)
  • Validation and error reporting

• Acceptance conditions

  • Expression algebra for omega-regular conditions
  • Classical acceptance types (Buchi, generalized-Buchi, co-Buchi, Rabin, Streett, Muller, Parity)
  • Finite-word acceptance for regular languages

• Pure structural interfaces

  • Base automaton interfaces without weighted semantics
  • NetworkX-based graph representations
  • Clean separation from quantitative monitoring (provided by automatix)

Architecture

Morphata serves as the foundation for the automatix library:

• morphata: Graph-based automata, HOA parsing, acceptance conditions
• automatix: Weighted automata over semirings (depends on morphata)
• algebraic: Pure semiring algebra (independent)

This layered architecture allows morphata to be used independently for structural automata operations, or as a foundation for weighted semantics.

Installation

Morphata is part of the automatix workspace. Install using uv:

uv pip install -e packages/morphata

Quick Example

from morphata.automata import NFA
from logic_asts import base

# Create an NFA
nfa = NFA[str]()
nfa.add_location(0, initial=True)
nfa.add_location(1, final=True)

# Add transition with guard
guard_a = base.Variable("a")
nfa.add_transition(0, 1, guard_a)

# Use the automaton
accepting, next_state = nfa({"a"}, nfa.initial_state)
print(f"Accepting: {accepting}, Next state: {next_state}")

HOA Parser Example

Standard HOA Format (Omega-Automata)

from morphata.hoa.parser import parse

hoa_string = """
HOA: v1
States: 2
Start: 0
acc-name: Buchi
Acceptance: 1 Inf(0)
AP: 1 "a"
--BODY--
State: 0
  [0] 1
State: 1 {0}
  [t] 1
--END--
"""

automaton = parse(hoa_string)
print(f"Acceptance: {automaton.header.acc}")

Extended Format: Finite-Word Acceptance

Morphata extends the HOA v1 format with a Final(n) operator for finite-word automata. This is not part of the standard HOA specification but provides a natural way to express finite-word acceptance in the HOA syntax.

from morphata.hoa.parser import parse

finite_hoa = """
HOA: v1
States: 2
Start: 0
acc-name: Finite
Acceptance: 1 Final(0)
AP: 1 "a"
--BODY--
State: 0
  [0] 1 {0}
  [!0] 0
State: 1
  [t] 1
--END--
"""

automaton = parse(finite_hoa)
# Accepts finite words ending with 'a'

Note: The Final(n) operator semantics differ from Fin(n) and Inf(n):

• Inf(n): Accept if acceptance set n is visited infinitely often (omega-regular)
• Fin(n): Accept if acceptance set n is visited finitely often (omega-regular)
• Final(n): Accept if the run ends in a state marked with acceptance set n (regular)

Development

Run tests:

python -m pytest packages/morphata/tests/ -v

Type checking:

python -m mypy packages/morphata/src/morphata/ --strict

License

Part of the automatix project.