2,265 research outputs found
Reachability Switching Games
We study the problem of deciding the winner of reachability switching games for zero-, one-, and two-player variants. Switching games provide a deterministic analogue of stochastic games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. Our results show that the switching variant of a game is harder in complexity-theoretic terms than the corresponding stochastic version
REACHABILITY SWITCHING GAMES
We study the problem of deciding the winner of reachability switching games
for zero-, one-, and two-player variants. Switching games provide a
deterministic analogue of stochastic games. We show that the zero-player case
is NL-hard, the one-player case is NP-complete, and that the two-player case is
PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness
for a succinctly-represented model that maintains the upper bound of NP
coNP. For the one- and two-player cases, our results hold in both the natural,
explicit model and succinctly-represented model. Our results show that the
switching variant of a game is harder in complexity-theoretic terms than the
corresponding stochastic version
Reachability Switching Games
We study the problem of deciding the winner of reachability switching games
for zero-, one-, and two-player variants. Switching games provide a
deterministic analogue of stochastic games. We show that the zero-player case
is NL-hard, the one-player case is NP-complete, and that the two-player case is
PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness
for a succinctly-represented model that maintains the upper bound of NP
coNP. For the one- and two-player cases, our results hold in both the natural,
explicit model and succinctly-represented model. Our results show that the
switching variant of a game is harder in complexity-theoretic terms than the
corresponding stochastic version
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets
We analyze the computational complexity of motion planning through local
"input/output" gadgets with separate entrances and exits, and a subset of
allowed traversals from entrances to exits, each of which changes the state of
the gadget and thereby the allowed traversals. We study such gadgets in the 0-,
1-, and 2-player settings, in particular extending past
motion-planning-through-gadgets work to 0-player games for the first time, by
considering "branchless" connections between gadgets that route every gadget's
exit to a unique gadget's entrance. Our complexity results include containment
in L, NL, P, NP, and PSPACE; as well as hardness for NL, P, NP, and PSPACE. We
apply these results to show PSPACE-completeness for certain mechanics in
Factorio, [the Sequence], and a restricted version of Trainyard, improving
prior results. This work strengthens prior results on switching graphs and
reachability switching games.Comment: 37 pages, 36 figure
Optimal Reachability in Divergent Weighted Timed Games
Weighted timed games are played by two players on a timed automaton equipped
with weights: one player wants to minimise the accumulated weight while
reaching a target, while the other has an opposite objective. Used in a
reactive synthesis perspective, this quantitative extension of timed games
allows one to measure the quality of controllers. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. Decidability results exist for subclasses of one-clock
games, and for a subclass with non-negative weights defined by a semantical
restriction on the weights of cycles. In this work, we introduce the class of
divergent weighted timed games as a generalisation of this semantical
restriction to arbitrary weights. We show how to compute their optimal value,
yielding the first decidable class of weighted timed games with negative
weights and an arbitrary number of clocks. In addition, we prove that
divergence can be decided in polynomial space. Last, we prove that for untimed
games, this restriction yields a class of games for which the value can be
computed in polynomial time
Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games
2.5 player parity games combine the challenges posed by 2.5 player
reachability games and the qualitative analysis of parity games. These two
types of problems are best approached with different types of algorithms:
strategy improvement algorithms for 2.5 player reachability games and recursive
algorithms for the qualitative analysis of parity games. We present a method
that - in contrast to existing techniques - tackles both aspects with the best
suited approach and works exclusively on the 2.5 player game itself. The
resulting technique is powerful enough to handle games with several million
states
- …