Tilings and patterns
Rational series and their languages
Rational series and their languages
Advances in Petri Nets 1988
Minimal (max,+) Realization of Convex Sequences
SIAM Journal on Control and Optimization
Automata, Languages, and Machines
Automata, Languages, and Machines
Optimal Allocation Sequences of Two Processes Sharing aResource
Discrete Event Dynamic Systems
Automata on Infinite Words, Ecole de Printemps d'Informatique Théorique,
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Complexity of cutting words on regular tilings
European Journal of Combinatorics
Extremal throughputs in free-choice nets
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
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In a heap model, solid blocks, or pieces, pile up according to the Tetris game mechanism. An optimal schedule is an infinite sequence of pieces minimizing the asymptotic growth rate of the heap. In a heap model with two pieces, we prove that there always exists an optimal schedule which is balanced, either periodic or Sturmian. We also consider the model where the successive pieces are chosen at random, independently and with some given probabilities. We study the expected growth rate of the heap. For a model with two pieces, the rate is either computed explicitly or given as an infinite series. We show an application for a system of two processes sharing a resource, and we prove that a greedy schedule is not always optimal.