Symbolic LTLf Synthesis

Zhu, Shufang; Tabajara, Lucas M.; Li, Jianwen; Pu, Geguang; Vardi, Moshe Y.

doi:10.24963/ijcai.2017/189

Cited by 66 publications

(83 citation statements)

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“…Following [27], we translate LTL f to a DFA using MONA [16]. LTL f is expressively equivalent to First-order Logic on finite words, which in turn is a fragment of Weak Second-order Theory of One Successor.…”

Section: Translation To Dfamentioning

confidence: 99%

LTLf Synthesis on Probabilistic Systems

Wells

Lahijanian

Kavraki

et al. 2020

Electron. Proc. Theor. Comput. Sci.

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Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTL f) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTL f to LTL and the second using native tools for LTL f. We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.

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Section: Translation To Dfamentioning

confidence: 99%

LTLf Synthesis on Probabilistic Systems

Wells

Lahijanian

Kavraki

et al. 2020

Electron. Proc. Theor. Comput. Sci.

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“…In this section we show how algorithms for synthesis under partial observability can be practically implemented within the context of existing tools for LTL f synthesis. We first review the SYFT framework [35], which represents the state-of-the-art for LTL f synthesis under full observability, combining an explicit automaton construction with symbolic BDD-based techniques for synthesizing the strategy efficiently. Then, we introduce novel versions of the two algorithms for partial observability that perform part of the automaton construction symbolically.…”

Section: Partial-observability Synthesis In Practicementioning

confidence: 99%

“…Finally, use a symbolic fixpoint algorithm to compute a winning strategy in the DFA game given by A. Details of each step can be found in [35].…”

Section: Partial-observability Synthesis In Practicementioning

confidence: 99%

“…This result completes the landscape of theoretical complexity presented in that work, which had proved tight bounds for DFA, AFW, and logical specifications. Second, we investigate how the two approaches for LTL f synthesis under partial observability discussed in [11] can be implemented in practice within the SYFT framework [35], which currently represents the state of the art in LTL f synthesis. Benefiting from SYFT's use of a symbolic synthesis algorithm, we implement the two approaches symbolically, potentially avoiding an exponential memory blowup.…”

Section: Introductionmentioning

confidence: 99%

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LTLf Synthesis under Partial Observability: From Theory to Practice

Tabajara

Vardi

2020

Electron. Proc. Theor. Comput. Sci.

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LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the difficulty of implementing such an extension in practice means that it has remained in the realm of theory. Recently, it has been demonstrated that restricting LTL synthesis to systems with finite executions by using LTL with finite-horizon semantics (LTL f) allows for significantly simpler implementations in practice. With the conceptual simplicity of LTL f , it becomes possible to explore extensions such as partial observability in practice for the first time. Previous work has analyzed the problem of LTL f synthesis under partial observability theoretically and suggested two possible algorithms, one with 3EXPTIME and another with 2EXPTIME complexity. In this work, we first prove a complexity lower bound conjectured in earlier work. Then, we complement the theoretical analysis by showing how the two algorithms can be integrated in practice into an established framework for LTL f synthesis. We furthermore identify a third, MSO-based, approach enabled by this framework. Our experimental evaluation reveals very different results from what the theory seems to suggest, with the 3EXPTIME algorithm often outperforming the 2EXP-TIME approach. Furthermore, as long as it is able to overcome an initial memory bottleneck, the MSO-based approach can often outperforms the others.

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“…Hence, progress in algorithms for these problems benefits a broad range of applications of formal methods. For example, typical algorithms for reactive synthesis reduce to computing the safe region of a safety game through repeated quantifier eliminations [1][2][3] or directly employ functional synthesis [4]. Until today, algorithms for quantifier elimination often involve (reduced ordered) Binary Decision Diagrams (BDDs) [5].…”

Section: Introductionmentioning

confidence: 99%

Incremental Determinization for Quantifier Elimination and Functional Synthesis

Rabe

2019

Computer Aided Verification

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Quantifier elimination and its cousin functional synthesis are fundamental problems in automated reasoning that could be used in many applications of formal methods. But, effective algorithms are still elusive. In this paper, we suggest a simple modification to a QBF algorithm to adapt it for quantifier elimination and functional synthesis. We demonstrate that the approach significantly outperforms previous algorithms for functional synthesis.

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Symbolic LTLf Synthesis

Cited by 66 publications

References 1 publication

LTLf Synthesis on Probabilistic Systems

LTLf Synthesis on Probabilistic Systems

LTLf Synthesis under Partial Observability: From Theory to Practice

Incremental Determinization for Quantifier Elimination and Functional Synthesis

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