Lower Bounds on the Area of Finite-State Machines

There a.re certain straightforward algorithms for laying out finite-state ma.chines . This pa.per shows that these algorithms are optimal in the worst case for machines with fixed alphabets. That is, for any s and k, there is a. deterministic finite-state machine with s states and k symbols such that any layout algorithm requires O(kslgs) area. to lay out its realization. Similarly, any layout algorithm requires O(ks2 ) area. in the worst case for nondeterministic finite-state ma.chines with s states and k symbols.