Composing system integrity using I/O automata

The I/O automata model of Lynch and Turtle (1987) is summarized and used to formalize several types of system integrity based on the control of transitions to invalid starts. Type-A integrity is exhibited by systems with no invalid initial states and that disallow transitions from valid reachable to invalid states. Type-B integrity is exhibited by systems that disallow externally-controlled transitions from valid reachable to invalid states, Type-C integrity is exhibited by systems that allow locally-controlled or externally-controlled transitions from reachable to invalid states. Strict-B integrity is exhibited by systems that are Type-B but not Type-A. Strict-C integrity is exhibited by systems that are Type-C but not Type-B. Basic results on the closure properties that hold under composition of systems exhibiting these types of integrity are presented in I/O automata-theoretic terms. Specifically, Type-A, Type-B, and Type-C integrity are shown to be composable, whereas Strict-B and Strict-C integrity are shown to not be generally composable. The integrity definitions and compositional results are illustrated using the familiar vending machine example specified as an I/O automaton and composed with a customer environment. The implications of the integrity definitions and compositional results on practical system design are discussed and a research plan for future work is outlined