The unwind property for programs with bounded memory

For programs that can access unbounded memory (e.g., flowchart programs with recursion on simple variable parameters), the ‘unwind property’ is equivalent to the ‘truth-table property’. For programs restricted to bounded memory (e.g., flowchart programs with parameterless recursion), the two properties are not equivalent in general. We recapitulate all known results, give new results, and establish conditions under which the two properties are equivalent for program with bounded memory.