The Complexity of LTL Rational Synthesis

Kupferman, Orna; Shenwald, Noam

doi:10.1007/978-3-030-99524-9_2

Cited by 6 publications

(2 citation statements)

References 20 publications

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“…Motivated by similar insights, other concepts of rationality have also been introduced in multi-player games, e.g. subgame perfect equilibria [29,7,28,10,6] or rational synthesis [20,22,18]. Similar to the implementations of SE by [13], these works restrict implementations to a single strategy profile.…”

Section: Contributionmentioning

confidence: 99%

Most General Winning Secure Equilibria Synthesis in Graph Games

Nayak,

Schmuck

2024

Lecture Notes in Computer Science

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This paper considers the problem of co-synthesis in k-player games over a finite graph where each player has an individual $$\omega $$ ω -regular specification $$\phi _i$$ ϕ i . In this context, a secure equilibrium (SE) is a Nash equilibrium w.r.t. the lexicographically ordered objectives of each player to first satisfy their own specification, and second, to falsify other players’ specifications. A winning secure equilibrium (WSE) is an SE strategy profile $$(\pi _i)_{i\in [1;k]}$$ ( π i ) i ∈ [ 1 ; k ] that ensures the specification $$\phi :=\bigwedge _{i\in [1;k]}\phi _i$$ ϕ : = ⋀ i ∈ [ 1 ; k ] ϕ i if no player deviates from their strategy $$\pi _i$$ π i . Distributed implementations generated from a WSE make components act rationally by ensuring that a deviation from the WSE strategy profile is immediately punished by a retaliating strategy that makes the involved players lose.In this paper, we move from deviation punishment in WSE-based implementations to a distributed, assume-guarantee based realization of WSE. This shift is obtained by generalizing WSE from strategy profiles to specification profiles$$(\varphi _i)_{i\in [1;k]}$$ ( φ i ) i ∈ [ 1 ; k ] with $$\bigwedge _{i\in [1;k]}\varphi _i = \phi $$ ⋀ i ∈ [ 1 ; k ] φ i = ϕ , which we call most general winning secure equilibria (GWSE). Such GWSE have the property that each player can individually pick a strategy $$\pi _i$$ π i winning for $$\varphi _i$$ φ i (against all other players) and all resulting strategy profiles $$(\pi _i)_{i\in [1;k]}$$ ( π i ) i ∈ [ 1 ; k ] are guaranteed to be a WSE. The obtained flexibility in players’ strategy choices can be utilized for robustness and adaptability of local implementations.Concretely, our contribution is three-fold: (1) we formalize GWSE for k-player games over finite graphs, where each player has an $$\omega $$ ω -regular specification $$\phi _i$$ ϕ i ; (2) we devise an iterative semi-algorithm for GWSE synthesis in such games, and (3) obtain an exponential-time algorithm for GWSE synthesis with parity specifications $$\phi _i$$ ϕ i .

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Section: Contributionmentioning

confidence: 99%

Most General Winning Secure Equilibria Synthesis in Graph Games

Nayak,

Schmuck

2024

Lecture Notes in Computer Science

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“…It is readily seen that the size of the unfolding of the arena defined above is exponential in the size of the original arena. On the other hand, solving the cooperative rational synthesis with LTL objectives is in 2EXPTIME in the size of the objectives formulas, and polynomial in the size of the arena [11,12]. It follows that our problem is 2EXPTIME when the counters are bounded.…”

Section: Bounded Resources and Decidabilitymentioning

confidence: 99%

Careful Autonomous Agents in Environments With Multiple Common Resources

Condurache

Dima

Jitaru

et al. 2022

Electron. Proc. Theor. Comput. Sci.

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Careful rational synthesis was defined in [7] as a quantitative extension of Fisman et al.'s rational synthesis [11], as a model of multi-agent systems in which agents are interacting in a graph arena in a turn-based fashion. There is one common resource, and each action may decrease or increase the resource. Each agent has a temporal qualitative objective and wants to maintain the value of the resource positive. One must find a Nash equilibrium. This problem is decidable.In more practical settings, the verification of the critical properties of multi-agent systems calls for models with many resources. Indeed, agents and robots consume and produce more than one type of resource: electric energy, fuel, raw material, manufactured goods, etc. We thus explore the problem of careful rational synthesis with several resources. We show that the problem is undecidable. We then propose a variant with bounded resources, motivated by the observation that in practical settings, the storage of resources is limited. We show that the problem becomes decidable, and is no harder than controller synthesis with Linear-time Temporal Logic objectives.

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A Game-Theoretic Approach for the Synthesis of Complex Systems

Bruyère

2022

Revolutions and Revelations in Computability

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The Complexity of LTL Rational Synthesis

Cited by 6 publications

References 20 publications

Most General Winning Secure Equilibria Synthesis in Graph Games

Most General Winning Secure Equilibria Synthesis in Graph Games

Careful Autonomous Agents in Environments With Multiple Common Resources

A Game-Theoretic Approach for the Synthesis of Complex Systems

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