Carbon standing stock distribution in the cuphotic zone of Lake Kinneret and the immediate fate of primary-produced carbon arc very different during late winter-early spring (with the occurrence of the annual dinollagellate bloom) than they are in late summer (when nanophytoplankton are the dominant primary producers). We used a linear programming model to construct balanced carbon flow charts for these two seasons based on measured primary productivity; on carbon standing stocks of algae, bacteria, flagellates, ciliates, cladocerans, rotifers, and fish; and on data on turnover times, respiration, and grazing rates obtained in 1989. The charts were compiled to fit as closely as possible all obscrvcd and inferred estimates of carbon fluxes while simultaneously ensuring that mass balance and key biological constraints were maintained for each of the 10 compartments representing the principal biota of the Kinneret food web. We used the model to examine the extent to which individual intercompartmental flux rates were free to vary while the mass-balance and biological constraints were enforced. The model was also capable of generating different yet feasible flow-chart scenarios; it thus proved useful in suggesting alternative hypotheses concerning the role of the microbial food web in the euphotic waters of Lake Kinneret.A major aim of both theoretical and applied aquatic research has long been to understand the patterns of flow of carbon and other elcments through the pelagic biota in lakes and seas. Within the last decade it has become increasingly evident that the complex communities of microbial organisms in the pelagic zone in both marine and freshwater environments play a key role in processing and transferring carbon, nitrogen, and phosphorus from primary producers to metazoan plankton and fish (Pomeroy 1974;Azam et al. 1983; Berman 1990). Much debate has been generated concerning the function of microbial food webs as Acknowledgments WC are indebted to B. Azoulai, K. D. Hambright, M. Gophen, G. Nahum, 0. Hadas, U. Pollinghcr, Y. 2. Yacobi, and T. Zohary for data, discussion, and dissent. We are grateful for the comments of two rcvicwcrs that enabled us to improve and revise the original version of the paper.

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1 2 .

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