Aspects of the Upper Bounds of Finite Input-Memory and Finite Output-Memory Sequential Machines

In this paper upper bounds on the finite input-memory μ
i
and finite output-memory μ
o
of n-state completely specified sequential machines (CSSM's) and incompletely specified sequential machines (ISSM's) are investigated. It is observed through computational means that N = n(n − 1)/2 is not a tight upper bound for finite input-memory of ISSM's and finite output-memory of both CSSM's and ISSM's. Tight upper bounds of μ
i
, μ
o
≤ 14 for 6-state machines and tight upper bounds of μ
i
, μ
o
, ≤ 20 for 7-state machines are obtained.