  We prove PSPACE-completeness of several reversible, fully deterministic
systems. At the core, we develop a framework for such proofs (building on a
result of Tsukiji and Hagiwara and a framework for motion planning through
gadgets), showing that any system that can implement three basic gadgets is
PSPACE-complete. We then apply this framework to four different systems,
showing its versatility. First, we prove that Deterministic Constraint Logic is
PSPACE-complete, fixing an error in a previous argument from 2008. Second, we
give a new PSPACE-hardness proof for the reversible `billiard ball' model of
Fredkin and Toffoli from 40 years ago, newly establishing hardness when only
two balls move at once. Third, we prove PSPACE-completeness of zero-player
motion planning with any reversible deterministic interacting $k$-tunnel gadget
and a `rotate clockwise' gadget (a zero-player analog of branching hallways).
Fourth, we give simpler proofs that zero-player motion planning is
PSPACE-complete with just a single gadget, the 3-spinner. These results should
in turn make it even easier to prove PSPACE-hardness of other reversible
deterministic systems.
