defensibility-analysis-shield-synthesis

name

defensibility-analysis-shield-synthesis

description

Network defensibility analysis using shield synthesis and adversarial game theory. Reinterprets shielded RL from runtime enforcement to design-time structural analysis. Use when: analyzing network topology security, synthesizing safety shields for RL agents, computing defensibility verdicts for cyber-physical systems, designing secure multi-agent architectures, evaluating network architecture defensibility, or combining formal verification with adversarial RL.

Defensibility Analysis via Shield Synthesis

Core Concept

Shield synthesis reinterpreted as a design-time analytical instrument rather than runtime enforcement. The automata-theoretic machinery (specification compilation, product game construction, attractor computation, winning-region extraction) produces structural insights about a system, not runtime constraints on deployed agents.

Methodology

Step 1: Two-Player Safety Game Construction

def construct_defense_game(network_topology, defender_spec, attacker_spec):
    """
    Build constrained two-player safety game for network defense.
    - Defender spec defines the unsafe region
    - Attacker spec restricts adversary legal actions during attractor computation
    """
    product_game = compile_specifications(network_topology, defender_spec, attacker_spec)
    winning_region = compute_attractor(product_game, attacker_restricted=True)
    return product_game, winning_region

Step 2: Defensibility Verdict

def compute_defensibility(winning_region, network_topology):
    """Compute formal certificate: defensible iff initial_state in winning_region"""
     network_topology.initial_state  winning_region