Jack W. Carlyle

State-calculable stochastic sequential machines, equivalences, and events

The observer/state-calculable stochastic machine is such that the present state, input, and output determine the next state. It is shown that since, for such machines, an initial state leads to degenerate terminal distributions, and reduction by merging equivalent states leads to unique reduced forms, several interrelated difficulties in stochastic machine theory are suppressed when attention is restricted to these structures. In particular, their input-output relations possess finitely many generalized states in an appropriate sense, and system realizations can be obtained from initial segments of such i-o relations. However, the need for considering input-output events in the stochastic case (rather than input-events only) is indicated even for observer/state-calculable structures.

The advantage of dynamic tuning in distributed asymmetric systems

An analytical performance modeling approach is presented for load sharing policies that schedule jobs based on a global system state. The main contributions of this work are: the derivation of analytical bounds to compute the average delay in large asymmetric systems under dynamic load sharing control, when job routing is based on the global system state; the experimental derivation of parameters which affect the implementation of load sharing policies at the user level; the demonstration that load sharing is effective even in the presence of high overheads; and the demonstration that in the asymmetric environment under study, carefully tuned algorithms for load sharing provide a significant improvement in performance over simpler algorithms.<<ETX>>

On a measure of complexity for stochastic sequential machines

The need for a measure different from the number of states in analyzing stochastic sequential machines is pointed out. Using the decomposition previously demonstrated in association with actual physical realization of stochastic sequential machines4, a particular measure of complexity C(M) for a given machine M is introduced. The computational aspect of C(M) is discussed and an example exhibiting two state-equivalent machines M1 and M2 with #{S1} ≫ #{S2} (#{Si} ≡ number of states of machine Mi i=1, 2) but C(M1) ≪ C(M2) is given. Areas for future research are pointed out.

Matching and spanning in certain planar graphs

AbstractCall a connected planar graphG legal if it has at least two nodes, no parallel edges or self-loops and at most two terminals (degree 1 nodes) and all terminals and degree 2 nodes are exterior. This class of graphs arose in connection with a two-dimensional generating system for modeling growth by binary cell division. Showing that any permitted pattern can be generated properly requires a matching or pairing lemma. The vertex set of a legal graph withn nodes can be split intop adjacent pairs ands singletons withs p, resulting in a matching which includes at least

Performance modeling and analysis for a large heterogeneous distributed system: UCLA-SEASnet

2\left[ {\frac{n}{3}} \right]

A load sharing interconnection network for hard real-time systems

nodes. This bound is sharp in the sense that there are legal graphs for which this matching is maximum. The matching can be implemented by a linear time algorithm. A legal graph witht terminals and n≥4 nodes has a spanning tree with at most

Special FOCS issue Sixteenth Annual Symposium on Foundations of Computer Science

\left[ {\frac{{n - t}}{2}} \right] + t