  The behavior and architecture of large scale discrete state systems found in
computer software and hardware can be specified and analyzed using a particular
class of primitive recursive functions. This paper begins with an illustration
of the utility of the method via a number of small examples and then via longer
specification and verification of the Paxos distributed consensus algorithm.
The sequence maps are then shown to provide an alternative representation of
deterministic state machines and algebraic products of state machines.
Distributed and composite systems, parallel and concurrent computation, and
real-time behavior can all be specified naturally with these methods - which
require neither extensions to the classical state machine model nor any
axiomatic methods or other techniques from formal methods. Compared to state
diagrams or tables or the standard set-tuple-transition-maps, sequence maps are
more concise and better suited to describing the behavior and compositional
architecture of computer systems. Staying strictly within the boundaries of
classical deterministic state machines anchors the methods to the algebraic
structures of automata and makes the specifications faithful to engineering
practice.
