The Hanoi Omega-Automata Format

Babiak, Tomáš; Blahoudek, František; Duret-Lutz, Alexandre; Klein, Joachim; Křetínský, Jan; Muller, David E.; Parker, David; Strejček, Jan

doi:10.1007/978-3-319-21690-4_31

Cited by 74 publications

(87 citation statements)

References 18 publications

(16 reference statements)

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“…Consequently, we use two ways of encoding states of the graph games as binary vectors. First, naive encoding, allowed by the fact that the output of tools such as [23,34] in HOA format [4] always assigns an id to each state. As this id is an integer, we may use its binary encoding.…”

Section: Random Ltlmentioning

confidence: 99%

Strategy Representation by Decision Trees in Reactive Synthesis

Brázdil

Chatterjee

Křetínský

et al. 2018

Tools and Algorithms for the Construction and Analysis of Systems

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Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with ω-regular winning conditions, specified as parity objectives, which can express properties such as safety, liveness, fairness, are the basic framework for verification and synthesis of reactive systems. The decisions for a player at various states of the graph game are represented as strategies. While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision diagrams (BDDs). However, due to the bit-level representation, BDDs do not retain the inherent flavor of the decisions of strategies, and are notoriously hard to minimize to obtain succinct representation. In this work we propose decision trees for strategy representation in graph games. Decision trees retain the flavor of decisions of strategies and allow entropy-based minimization to obtain succinct trees. However, decision trees work in settings (e.g., probabilistic models) where errors are allowed, and overfitting of data is typically avoided. In contrast, for strategies in graph games no error is allowed, and the decision tree must represent the entire strategy. We develop new techniques to extend decision trees to overcome the above obstacles, while retaining the entropybased techniques to obtain succinct trees. We have implemented our techniques to extend the existing decision tree solvers. We present experimental results for problems in reactive synthesis to show that decision trees provide a much more efficient data-structure for strategy representation as compared to BDDs.

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Section: Random Ltlmentioning

confidence: 99%

Strategy Representation by Decision Trees in Reactive Synthesis

Brázdil

Chatterjee

Křetínský

et al. 2018

Tools and Algorithms for the Construction and Analysis of Systems

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“…We implemented the construction described in the previous sections in a tool named MUNGOJERRIE [8], which reads MDPs described in the PRISM language [13], and ωregular automata written in the HOA format [1,6]. MUNGOJERRIE builds the product M ζ , provides an interface for RL algorithms akin to that of [4] and supports probabilistic model checking.…”

Section: Resultsmentioning

confidence: 99%

“…If p σ s (ζ) = 1 then no rejecting BSCC is reachable from s in (M × A) σ and a σ s = 1.Proof (1). holds as there are no accepting transition in a rejecting BSCC of (M×A) σ , and so t cannot be reached when starting at s in M ζ .…”

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confidence: 97%

Omega-Regular Objectives in Model-Free Reinforcement Learning

Hahn

Perez

Schewe

et al. 2019

Lecture Notes in Computer Science

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We provide the first solution for model-free reinforcement learning of ω-regular objectives for Markov decision processes (MDPs). We present a constructive reduction from the almost-sure satisfaction of ω-regular objectives to an almostsure reachability problem, and extend this technique to learning how to control an unknown model so that the chance of satisfying the objective is maximized. A key feature of our technique is the compilation of ω-regular properties into limitdeterministic Büchi automata instead of the traditional Rabin automata; this choice sidesteps difficulties that have marred previous proposals. Our approach allows us to apply model-free, off-the-shelf reinforcement learning algorithms to compute optimal strategies from the observations of the MDP. We present an experimental evaluation of our technique on benchmark learning problems.An ω-word w on an alphabet Σ is a function w : N → Σ. We abbreviate w(i) by w i . The set of ω-words on Σ is written Σ ω and a subset of Σ ω is an ω-language on Σ.A probability distribution over a finite set S is a function d : S→[0, 1] such that s∈S d(s) = 1. Let D(S) denote the set of all discrete distributions over S. We say a distribution d ∈ D(S) is a point distribution if d(s)=1 for some s ∈ S. For a distribution d ∈ D(S) we write supp(d) def = {s ∈ S : d(s) > 0}.

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“…All the previously mentioned acceptance conditions can be expressed by a generic acceptance condition originally introduced by Emerson and Lei [10] and recently reinvented in the Hanoi omega-automata (HOA) format [1]. Emerson-Lei acceptance condition is any positive boolean formula over terms of the form Inf and Fin , where is an acceptance mark.…”

Section: Introductionmentioning

confidence: 99%

LTL to Smaller Self-Loop Alternating Automata and Back

Blahoudek

Major

Strejček

2019

Theoretical Aspects of Computing – ICTAC 2019

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Self-loop alternating automata (SLAA) with Büchi or co-Büchi acceptance are popular intermediate formalisms in translations of LTL to deterministic or nondeterministic automata. This paper considers SLAA with generic transition-based Emerson-Lei acceptance and presents translations of LTL to these automata and back. Importantly, the translation of LTL to SLAA with generic acceptance produces considerably smaller automata than previous translations of LTL to Büchi or co-Büchi SLAA. Our translation is already implemented in the tool LTL3TELA, where it helps to produce small deterministic or nondeterministic automata for given LTL formulae.

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The Hanoi Omega-Automata Format

Cited by 74 publications

References 18 publications

Strategy Representation by Decision Trees in Reactive Synthesis

Strategy Representation by Decision Trees in Reactive Synthesis

Omega-Regular Objectives in Model-Free Reinforcement Learning

LTL to Smaller Self-Loop Alternating Automata and Back

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