Boolean / Logic in DP Transitions

Boolean logic combining conditions—AND of reachable flags, OR of ways—must match counting vs optimization semantics.

Why this shows up in the real world

Feature flags in config compilers combine predicates. Access policies compose rules.

Core idea (explained for students)

Use separate DP tables for AND vs OR; for counting AND multiply independent components only when truly independent.

Try this in Python

def and_or_ways(a: bool, b: bool) -> tuple[int, int]:
    and_w = 1 if a and b else 0
    or_w = 1 if a or b else 0
    return and_w, or_w


print(and_or_ways(True, False))

Common mistakes

• Multiplying dependent probabilities.
• XOR confusion with addition.

Key takeaways

• Truth tables for tiny state machines in tests.