We look at a simple, but general model, of a systolic system called a trellis automaton (TA). A TA is equivalent in computational power to a one-dimensional unbounded cellular automaton (CA), a model of parallel computation which has been studied extensively in the literature. Different varieties of TA’s are equivalent to corresponding variations of CA’s. We present, for the first time, sequential machine characterizations of TA’s (CA’s). The sequential machines are useful and powerful tools for investigating properties of TA’s (CA’s). They ar easy to program because, unlike the parallel models, one does not have to deal with the problem of synchronization. Several applications are given. In particular, we prove a new speed-up theorem which is stronger than what has previously been shown.
[1]
Wolfgang J. Paul,et al.
On time hierarchies
,
1977,
STOC '77.
[2]
Oscar H. Ibarra,et al.
Characterizations and Computational Complexity of Systolic Trellis Automata
,
1984,
Theor. Comput. Sci..
[3]
Stephen N. Cole.
Real-Time Computation by n-Dimensional Iterative Arrays of Finite-State Machines
,
1969,
IEEE Trans. Computers.
[4]
Arto Salomaa,et al.
Systolic Trellis Automata: Stability, Decidability and Complexity
,
1986,
Inf. Control..
[5]
Charles E. Leiserson,et al.
Optimizing synchronous systems
,
1981,
22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).