On Satisficing in Quantitative Games

Bansal, Suguman; Chatterjee, Krishnendu; Vardi, Moshe Y.

doi:10.26226/morressier.604907f41a80aac83ca25ce8

Cited by 2 publications

(3 citation statements)

References 25 publications

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“…However, the converse direction is still open: Are functions with ω-regular comparators also ω-regular? We showed that ω-regular comparators not only yield generic algorithms for problems including quantitative inclusion and winning strategies in incomplete-information quantitative games, they also result in algorithmic advances [BCV21]. We establish that when the weights are represented in unary, the discounted-sum inclusion problem is PSAPCE-complete for integer discount-factor, hence closing a complexity gap.…”

Section: Discussionmentioning

confidence: 86%

Comparator automata in quantitative verification

Bansal¹,

Chaudhuri²,

Vardi³

2022

Logical Methods in Computer Science

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The notion of comparison between system runs is fundamental in formal verification. This concept is implicitly present in the verification of qualitative systems, and is more pronounced in the verification of quantitative systems. In this work, we identify a novel mode of comparison in quantitative systems: the online comparison of the aggregate values of two sequences of quantitative weights. This notion is embodied by comparator automata (comparators, in short), a new class of automata that read two infinite sequences of weights synchronously and relate their aggregate values. We show that aggregate functions that can be represented with B\"uchi automaton result in comparators that are finite-state and accept by the B\"uchi condition as well. Such $\omega$-regular comparators further lead to generic algorithms for a number of well-studied problems, including the quantitative inclusion and winning strategies in quantitative graph games with incomplete information, as well as related non-decision problems, such as obtaining a finite representation of all counterexamples in the quantitative inclusion problem. We study comparators for two aggregate functions: discounted-sum and limit-average. We prove that the discounted-sum comparator is $\omega$-regular iff the discount-factor is an integer. Not every aggregate function, however, has an $\omega$-regular comparator. Specifically, we show that the language of sequence-pairs for which limit-average aggregates exist is neither $\omega$-regular nor $\omega$-context-free. Given this result, we introduce the notion of prefix-average as a relaxation of limit-average aggregation, and show that it admits $\omega$-context-free comparators i.e. comparator automata expressed by B\"uchi pushdown automata.

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Section: Discussionmentioning

confidence: 86%

Comparator automata in quantitative verification

Bansal¹,

Chaudhuri²,

Vardi³

2022

Logical Methods in Computer Science

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“…with discount factor d > 1 is given by DS (W, d) = ∞ i=0 wi d i . The comparator automata for the discounted-sum has been shown to be a safety or co-safety automata when the discount factor d > 1 is an integer, for all values of R, µ and v. It is further known to not form a Büchi automata for non-integer discount factors d > 1, for all values of R, µ and v (Bansal and Vardi 2019;Bansal, Chatterjee, and Vardi 2021).…”

Section: Preliminariesmentioning

confidence: 99%

“…the threshold value. The advantage of this approach is that when the discount factor is an integer, an existing synthesis algorithm is both sound and complete (Bansal, Chatterjee, and Vardi 2021). The method builds on novel automata-based technique for quantitative reasoning called comparator automata (Bansal, Chaudhuri, and Vardi 2018a,b).…”

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confidence: 99%

Synthesis from Satisficing and Temporal Goals

Bansal¹,

Kavraki²,

Vardi³

et al. 2022

Preprint

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Reactive synthesis from high-level specifications that combine hard constraints expressed in Linear Temporal Logic (LTL) with soft constraints expressed by discounted-sum (DS) rewards has applications in planning and reinforcement learning. An existing approach combines techniques from LTL synthesis with optimization for the DS rewards but has failed to yield a sound algorithm. An alternative approach combining LTL synthesis with satisficing DS rewards (rewards that achieve a threshold) is sound and complete for integer discount factors, but, in practice, a fractional discount factor is desired. This work extends the existing satisficing approach, presenting the first sound algorithm for synthesis from LTL and DS rewards with fractional discount factors. The utility of our algorithm is demonstrated on robotic planning domains. IntroductionReactive synthesis is the automated construction, from a high-level description of its desired behavior, of a reactive system that continuously interacts with an uncontrollable external environment (Church 1957).Recent applications of reactive synthesis have emerged in AI for planning and robotics tasks (Camacho, Bienvenu, and McIlraith 2019;He et al. 2019;Kress-Gazit, Lahijanian, and Raman 2018). These applications can be formulated as a deterministic turn-based interaction between a controllable system player and an uncontrollable environment player. Given a specification, the synthesis task is to generate a system strategy such that all resulting interactions with the environment satisfy the specification. A large focus in this line of work has been on synthesis from Linear Temporal Logic (LTL) specifications (Pnueli 1977;Pnueli and Rosner 1989).Yet, several desired specifications either cannot be expressed using LTL or doing is cumbersome. Examples include specifications about the quantitative properties of systems, such as rewards, costs, degrees of satisfaction, and so on. In fact, the combination of LTL with quantitative properties is used to express more nuanced and complex specifications (see Figure 1). Subsequently, synthesis algorithms from combination specifications have followed (

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On Satisficing in Quantitative Games

Cited by 2 publications

References 25 publications

Comparator automata in quantitative verification

Comparator automata in quantitative verification

Synthesis from Satisficing and Temporal Goals

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