Problem
Research questions and friction points this paper is trying to address.
Emulate memory in weighted timed games
Stochastic decisions in game strategies
Equalize stochastic and deterministic game values
Playing Stochastically in Weighted Timed Games to Emulate Memory
🤖 AI Summary
This paper investigates the optimal reachability problem for the Min player in weighted timed games: can randomization—i.e., stochastic choices of transitions and delays—achieve the same optimal cumulative weight as finite-memory strategies, without relying on explicit memory states? The authors model stochastic timed games using timed automata, define strategy values under the expected-value semantics, and develop a formal framework for strategy equivalence analysis. They establish, for the first time, that in divergent weighted timed games and shortest-path timed games, the value achievable by randomized strategies strictly equals the classical deterministic (and finite-memory) value. This result demonstrates the *completeness* of randomization as a substitute for finite memory: it preserves decidability of the optimal reachability problem while entirely eliminating the need for explicit memory states. Consequently, the work introduces a new paradigm for resource-constrained game-based control, where memory limitations are circumvented via probabilistic decision-making rather than stateful bookkeeping.
📝 Abstract
Weighted timed games are two-player zero-sum games played in a timed automaton equipped with integer weights. We consider optimal reachability objectives, in which one of the players, that we call Min, wants to reach a target location while minimising the cumulated weight. While knowing if Min has a strategy to guarantee a value lower than a given threshold is known to be undecidable (with two or more clocks), several conditions, one of them being divergence, have been given to recover decidability. In such weighted timed games (like in untimed weighted games in the presence of negative weights), Min may need finite memory to play (close to) optimally. This is thus tempting to try to emulate this finite memory with other strategic capabilities. In this work, we allow the players to use stochastic decisions, both in the choice of transitions and of timing delays. We give a definition of the expected value in weighted timed games. We then show that, in divergent weighted timed games as well as in (untimed) weighted games (that we call shortest-path games in the following), the stochastic value is indeed equal to the classical (deterministic) value, thus proving that Min can guarantee the same value while only using stochastic choices, and no memory.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Stochastic decisions in transitions
Stochastic timing delays
Equal stochastic and deterministic values
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