Browsing by Author "Bansal, Suguman"

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    Algorithmic analysis of Regular repeated games
    (2016-09-15) Bansal, Suguman; Chaudhuri, Swarat
    The problem on computing rational behaviors in multi-agent systems with selfish agents (Games) has become paramount for the analysis of such systems. {\em Nash equilibria} is one of the most central notions of rational behavior. While the problem of computing Nash equilibria in simple games is well understood, the same cannot be said for more complex games. {\em Repeated games} are one such class of games. In this thesis, we introduce {\em regular repeated games} as a model for repeated games with bounded rationality. In regular repeated games, agent strategies are given by weighted (discounted-sum aggregate), non-deterministic B\"uchi transducers. We design an algorithm {\ComputeNash} to compute all Nash equilibria in a regular repeated game. The crux of the algorithm lies in determining if a strategy profile is in Nash equilibria or not. For this it is necessary to compare the discounted sum on one infinite execution with that one other executions. Such relational reasoning has not been studies in the literature before. To this end, we introduce the concept of an {\em $\omega$-regular comparators}. We demonstrate promise of our approach via experimental analysis on case studies: Iterated Prisoner's Dilemma, repeated auctions, and a model of the Bitcoin protocol.
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    Automata-Based Quantitative Verification
    (2020-05-13) Bansal, Suguman; Vardi, Moshe Y
    The analysis of quantitative properties of computing systems, or quantitative analysis in short, is an emerging area in automated formal analysis. Such properties address aspects such as costs and rewards, quality measures, resource consumption, distance metrics, and the like. So far, several applications of quantitative analysis have been identified, including formal guarantees for reinforcement learning, planning under resource constraints, and verification of (multi-agent) on-line economic protocols. Existing solution approaches for problems in quantitative analysis suffer from two challenges that adversely impact the theoretical understanding of quantitative analysis, and large-scale applicability due to limitations on scalability. These are the lack of generalizability, and {separation-of-techniques. Lack of generalizability refers to the issue that solution approaches are often specialized to the underlying cost model that evaluates the quantitative property. Different cost models deploy such disparate algorithms that there is no transfer of knowledge from one cost model to another. Separation-of-techniques refers to the inherent dichotomy in solving problems in quantitative analysis. Most algorithms comprise of two phases: A structural phase, which reasons about the structure of the quantitative system(s) using techniques from automata or graphs; and a numerical phase, which reasons about the quantitative dimension/cost model using numerical methods. The techniques used in both phases are so unlike each other that they are difficult to combine, forcing the phases to be performed sequentially, thereby impacting scalability. This thesis contributes towards a novel framework that addresses these challenges. The introduced framework, called comparator automata or comparators in short, builds on automata-theoretic foundations to generalize across a variety of cost models. The crux of comparators is that they enable automata-based methods in the numerical phase, hence eradicating the dependence on numerical methods. In doing so, comparators are able to integrate the structural and numerical phases. On the theoretical front, we demonstrate that comparator-based solutions have the advantage of generalizable results, and yield complexity-theoretic improvements over a range of problems in quantitative analysis. On the practical front, we demonstrate through empirical analysis that comparator-based solutions render more efficient, scalable, and robust performance, and hold the ability to integrate quantitative with qualitative objectives.
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    Comparator automata in quantitative verification
    (EPI Sciences, 2022) Vardi, Moshe Y.; Chaudhuri, Swarat; Bansal, Suguman
    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.