Improved Algorithms for One-Pair and k-Pair Streett Objectives

Chatterjee, Krishnendu; Henzinger, Monika; Loitzenbauer, Veronika

doi:10.1109/lics.2015.34

Cited by 11 publications

(18 citation statements)

References 57 publications

(127 reference statements)

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“…After decades of algorithmic improvements for the modal mu-calculus model checking [8], [3], [26] and for solving parity games [13], [15], [25], [5], [21], a recent breakthrough came from Calude et al [4] who gave the first algorithm that works in quasi-polynomial time, where the best upper bounds known previously were subexponential of the form n O( √ n) [15], [21]. Remarkably, Calude et al have also established fixed parameter tractability for the key parameter d-the number of distinct vertex priorities.…”

Section: A Parity Gamesmentioning

confidence: 99%

Succinct progress measures for solving parity games

Jurdziński

Lazić

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

167

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Section: A Parity Gamesmentioning

confidence: 99%

Succinct progress measures for solving parity games

Jurdziński

Lazić

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

167

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“…Both can happen at most O(n) times, thus there can be at most O(n) iterations of the outer while-loop. The Pre and Post operations at lines 12,30,33,34,35, and 36 can be charged to the iterations of the outer while-loop.…”

Section: Invariant 8 (No Random Outgoing Edges)mentioning

confidence: 99%

Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives

Chatterjee

Henzinger

Loitzenbauer

et al. 2018

Computer Aided Verification

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Given a model and a specification, the fundamental model-checking problem asks for algorithmic verification of whether the model satisfies the specification. We consider graphs and Markov decision processes (MDPs), which are fundamental models for reactive systems. One of the very basic specifications that arise in verification of reactive systems is the strong fairness (aka Streett) objective. Given different types of requests and corresponding grants, the objective requires that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All ω-regular objectives can be expressed as Streett objectives and hence they are canonical in verification. To handle the state-space explosion, symbolic algorithms are required that operate on a succinct implicit representation of the system rather than explicitly accessing the system. While explicit algorithms for graphs and MDPs with Streett objectives have been widely studied, there has been no improvement of the basic symbolic algorithms. The worst-case numbers of symbolic steps required for the basic symbolic algorithms are as follows: quadratic for graphs and cubic for MDPs. In this work we present the first sub-quadratic symbolic algorithm for graphs with Streett objectives, and our algorithm is sub-quadratic even for MDPs. Based on our algorithmic insights we present an implementation of the new symbolic approach and show that it improves the existing approach on several academic benchmark examples.

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“…Algorithm StreettMDPdense combines Algorithm StreettMDPimpr with the ideas of the MEC-algorithm for dense MDPs of [16] and the algorithm for graphs with Streett objectives of [17]. The difference to Algorithm StreettMDPimpr lies in the search for strongly connected components.…”

Section: Algorithm For Dense Mdps With Streett Objectivesmentioning

confidence: 99%

“…Second, we consider conjunctive and disjunctive safety objectives and queries. The following results are known: the conjunctive problem can be reduced to a single objective and can be solved in linear time, both in Streett O(min(n 2 , m √ m log n, km) + b log n) [28,17] graphs and MDPs (see e.g. [14]); disjunctive queries for MDPs can be solved in O(k · m) time; and disjunctive objectives for MDPs are PSPACE-complete [23].…”

Section: Introductionmentioning

confidence: 99%

Model and Objective Separation with Conditional Lower Bounds

Chatterjee

Dvořák

Henzinger

et al. 2016

Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science

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Given a model of a system and an objective, the model-checking question asks whether the model satisfies the objective. We study polynomial-time problems in two classical models, graphs and Markov Decision Processes (MDPs), with respect to several fundamental ω-regular objectives, e.g., Rabin and Streett objectives. For many of these problems the best-known upper bounds are quadratic or cubic, yet no super-linear lower bounds are known. In this work our contributions are two-fold: First, we present several improved algorithms, and second, we present the first conditional super-linear lower bounds based on widely believed assumptions about the complexity of CNF-SAT and combinatorial Boolean matrix multiplication. A separation result for two models with respect to an objective means a conditional lower bound for one model that is strictly higher than the existing upper bound for the other model, and similarly for two objectives with respect to a model. Our results establish the following separation results: (1) A separation of models (graphs and MDPs) for disjunctive queries of reachability and Büchi objectives. (2) Two kinds of separations of objectives, both for graphs and MDPs, namely, (2a) the separation of dual objectives such as reachability/safety (for disjunctive questions) and Streett/Rabin objectives, and (2b) the separation of conjunction and disjunction of multiple objectives of the same type such as safety, Büchi, and coBüchi. In summary, our results establish the first model and objective separation results for graphs and MDPs for various classical ω-regular objectives. Quite strikingly, we establish conditional lower bounds for the disjunction of objectives that are strictly higher than the existing upper bounds for the conjunction of the same objectives. 1 In particular improvements by polylogarithmic factors are not excluded. 2 Combinatorial here means avoiding fast matrix multiplication [33], see also the discussion in [27].2 objectives and their dual Rabin objectives [39]. A one-pair Streett objective for two sets of vertices L and U specifies that if the Büchi objective for target set L is satisfied, then also the Büchi objective for target set U has to be satisfied; in other words, a one-pair Streett objective is the disjunction of a coBüchi objective (with target set L) and a Büchi objective (with target set U ). The dual one-pair Rabin objective for two vertex sets L and U is the conjunction of a Büchi objective with target set L and a coBüchi objective with target set U . A Streett objective is the conjunction of k one-pair Streett objectives and its dual Rabin objective is the disjunction of k one-pair Rabin objectives. Algorithmic questions. The algorithmic question given a model and an objective is as follows: (a) for standard graphs, the model-checking question asks whether there is a path that satisfies the objective; and (b) for MDPs, the basic model-checking question asks whether there is a policy (or a strategy that resolves the non-deterministic choices of outgoing edges) for player...

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Improved Algorithms for One-Pair and k-Pair Streett Objectives

Cited by 11 publications

References 57 publications

Succinct progress measures for solving parity games

Succinct progress measures for solving parity games

Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives

Model and Objective Separation with Conditional Lower Bounds

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