67 research outputs found
Games with recurring certainty
Infinite games where several players seek to coordinate under imperfect
information are known to be intractable, unless the information flow is
severely restricted. Examples of undecidable cases typically feature a
situation where players become uncertain about the current state of the game,
and this uncertainty lasts forever. Here we consider games where the players
attain certainty about the current state over and over again along any play.
For finite-state games, we note that this kind of recurring certainty implies a
stronger condition of periodic certainty, that is, the events of state
certainty ultimately occur at uniform, regular intervals. We show that it is
decidable whether a given game presents recurring certainty, and that, if so,
the problem of synthesising coordination strategies under w-regular winning
conditions is solvable.Comment: In Proceedings SR 2014, arXiv:1404.041
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
Quantum Interactive Proofs with Competing Provers
This paper studies quantum refereed games, which are quantum interactive
proof systems with two competing provers: one that tries to convince the
verifier to accept and the other that tries to convince the verifier to reject.
We prove that every language having an ordinary quantum interactive proof
system also has a quantum refereed game in which the verifier exchanges just
one round of messages with each prover. A key part of our proof is the fact
that there exists a single quantum measurement that reliably distinguishes
between mixed states chosen arbitrarily from disjoint convex sets having large
minimal trace distance from one another. We also show how to reduce the
probability of error for some classes of quantum refereed games.Comment: 13 pages, to appear in STACS 200
Lossy Channel Games under Incomplete Information
In this paper we investigate lossy channel games under incomplete
information, where two players operate on a finite set of unbounded FIFO
channels and one player, representing a system component under consideration
operates under incomplete information, while the other player, representing the
component's environment is allowed to lose messages from the channels. We argue
that these games are a suitable model for synthesis of communication protocols
where processes communicate over unreliable channels. We show that in the case
of finite message alphabets, games with safety and reachability winning
conditions are decidable and finite-state observation-based strategies for the
component can be effectively computed. Undecidability for (weak) parity
objectives follows from the undecidability of (weak) parity perfect information
games where only one player can lose messages.Comment: In Proceedings SR 2013, arXiv:1303.007
Two-Person Stochastic Duel with Energy Fuel Constraint Ammo
This paper deals a novel variation of the versatile stochastic duel game,
which incorporates an energy fuel constraint in a two-player duel game. The
energy fuel not only measures the vitality of players but also determines the
power of the shooting projectile. The game requires players to carefully
balance their energy usage while trying to outmaneuver their opponent. This
unique theoretical framework of the stochastic game model provides a valuable
method for understanding strategic behavior in competitive environments,
particularly in decision-making scenarios with fluctuation processes. The
proposed game provides players with the challenge of optimizing their energy
fuel usage while managing the risk of losing the game. The unique rules and
constraints of the game in this research are expected for contributing insights
into the decision-making strategies and behaviors of players in a wide range of
practical applications.Comment: Song-Kyoo Kim, Two-Person Stochastic Duel with Energy Fuel Constraint
Ammo, Mathematics 11:7 (2023), 362
Computing Weakest Strategies for Safety Games of Imperfect Information
CEDAR (Counter Example Driven Antichain Refinement) is a new symbolic algorithm for computing weakest strategies for safety games of imperfect information. The algorithm computes a fixed point over the lattice of contravariant antichains. Here contravariant antichains are antichains over pairs consisting of an information set and an allow set representing the associated move. We demonstrate how the richer structure of contravariant antichains for representing antitone functions, as opposed to standard antichains for representing sets of downward closed sets, allows CEDAR to apply a significantly less complex controllable predecessor step than previous algorithms
Non-Cooperative Rational Interactive Proofs
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to design protocols for computation outsourcing.
Existing interactive-proof games largely fall into two categories: either as games of cooperation such as multi-prover interactive proofs and cooperative rational proofs, where the provers work together as a team; or as games of conflict such as refereed games, where the provers directly compete with each other in a zero-sum game. Neither of these extremes truly capture the strategic nature of service providers in outsourcing applications. How to design and analyze non-cooperative interactive proofs is an important open problem.
In this paper, we introduce a mechanism-design approach to define a multi-prover interactive-proof model in which the provers are rational and non-cooperative - they act to maximize their expected utility given others\u27 strategies. We define a strong notion of backwards induction as our solution concept to analyze the resulting extensive-form game with imperfect information.
We fully characterize the complexity of our proof system under different utility gap guarantees. (At a high level, a utility gap of u means that the protocol is robust against provers that may not care about a utility loss of 1/u.) We show, for example, that the power of non-cooperative rational interactive proofs with a polynomial utility gap is exactly equal to the complexity class P^{NEXP}
POMDPs under Probabilistic Semantics
We consider partially observable Markov decision processes (POMDPs) with
limit-average payoff, where a reward value in the interval [0,1] is associated
to every transition, and the payoff of an infinite path is the long-run average
of the rewards. We consider two types of path constraints: (i) quantitative
constraint defines the set of paths where the payoff is at least a given
threshold lambda_1 in (0,1]; and (ii) qualitative constraint which is a special
case of quantitative constraint with lambda_1=1. We consider the computation of
the almost-sure winning set, where the controller needs to ensure that the path
constraint is satisfied with probability 1. Our main results for qualitative
path constraint are as follows: (i) the problem of deciding the existence of a
finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding
the existence of an infinite-memory controller is undecidable. For quantitative
path constraint we show that the problem of deciding the existence of a
finite-memory controller is undecidable.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Observation and Distinction. Representing Information in Infinite Games
We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata.
The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists
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