Rabinizer 4: From LTL to Your Favourite Deterministic Automaton

Křetínský, Jan; Meggendorfer, Tobias; Sickert, Salomon; Ziegler, Christopher

doi:10.1007/978-3-319-96145-3_30

Cited by 33 publications

(41 citation statements)

References 38 publications

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“…The practical relevance of these constructions and their precursors has been demonstrated by tools, too, as the reduced size of the automata plays the crucial role in speeding up LTL verification and synthesis. The tool Rabinizer [48] implements all these constructions. Its inception [27,46] with the generalised Rabin condition [45] and integration [13,41] into the probabilistic model checker PRISM [44] has led to the development of the standard HOA format [4] for ω-automata, covering less standard conditions, and to the extension of PRISM allowing for external LTL-to-HOA translators.…”

Section: Discussionmentioning

confidence: 99%

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A Unified Translation of Linear Temporal Logic to ω-Automata

Esparza

Křetínský

Sickert

2020

J. ACM

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We present a unified translation of linear temporal logic (LTL) formulas into deterministic Rabin automata (DRA), limit-deterministic Büchi automata (LDBA), and nondeterministic Büchi automata (NBA). The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive Boolean combination of languages that can be translated into ω-automata by elementary means. In particular, Safra's, ranking, and breakpoint constructions used in other translations are not needed. We further give evidence that this theoretical clean and compositional approach does not lead to large automata per se and in fact in the case of DRAs yields significantly smaller automata compared to the previously known approach using determinisation of NBAs. CCS Concepts: • Theory of computation → Automata over infinite objects; Modal and temporal logics;

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Section: Discussionmentioning

confidence: 99%

“…Thus, one can argue that it is the state-of-the-art portfolio translator. • ltl2dgra (asymmetric, [48], Owl 20.06). 9 This direct translation to DRAs and DGRAs has been described in Reference [20] and revised and corrected in Reference [22].…”

Section: Methodsmentioning

confidence: 99%

A Unified Translation of Linear Temporal Logic to ω-Automata

Esparza

Křetínský

Sickert

2020

J. ACM

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“…The number of states in this automaton is doubly exponential in the size of AP . However, efficient implementations and heuristics effectively reduce the number of states (Kretínský et al, 2018).…”

Section: Specificationsmentioning

confidence: 99%

Task-Aware Verifiable RNN-Based Policies for Partially Observable Markov Decision Processes

Carr

Jansen

Topcu

2021

jair

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Partially observable Markov decision processes (POMDPs) are models for sequential decision-making under uncertainty and incomplete information. Machine learning methods typically train recurrent neural networks (RNN) as effective representations of POMDP policies that can efficiently process sequential data. However, it is hard to verify whether the POMDP driven by such RNN-based policies satisfies safety constraints, for instance, given by temporal logic specifications. We propose a novel method that combines techniques from machine learning with the field of formal methods: training an RNN-based policy and then automatically extracting a so-called finite-state controller (FSC) from the RNN. Such FSCs offer a convenient way to verify temporal logic constraints. Implemented on a POMDP, they induce a Markov chain, and probabilistic verification methods can efficiently check whether this induced Markov chain satisfies a temporal logic specification. Using such methods, if the Markov chain does not satisfy the specification, a byproduct of verification is diagnostic information about the states in the POMDP that are critical for the specification. The method exploits this diagnostic information to either adjust the complexity of the extracted FSC or improve the policy by performing focused retraining of the RNN. The method synthesizes policies that satisfy temporal logic specifications for POMDPs with up to millions of states, which are three orders of magnitude larger than comparable approaches.

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“…The construction of A ¬φ can also be carried out in Rabinizer4 [25]. The accepting runs of A ¬φ of length less than or equal to N can be computed using a depth-first search algorithm [47].…”

Section: Automaton-based Verificationmentioning

confidence: 99%

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Ramasubramanian

Niu

Clark

et al. 2019

Lecture Notes in Computer Science

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This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in sa f e − LTL F , a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discretetime dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximizes the probability of satisfaction of a sa f e − LTL F formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach.

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Rabinizer 4: From LTL to Your Favourite Deterministic Automaton

Cited by 33 publications

References 38 publications

A Unified Translation of Linear Temporal Logic to ω-Automata

A Unified Translation of Linear Temporal Logic to ω-Automata

Task-Aware Verifiable RNN-Based Policies for Partially Observable Markov Decision Processes

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

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