Owl: A Library for $$\omega $$-Words, Automata, and LTL

Křetínský, Jan; Meggendorfer, Tobias; Sickert, Salomon

doi:10.1007/978-3-030-01090-4_34

Cited by 62 publications

(60 citation statements)

References 34 publications

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“…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. Support for such constructions is then accessible in the reusable library Owl [47]; it distils the key functionalities of Rabinizer, which is a tool for end-users of LTL, into reusable modules and adds further support for developers. Further, MoChiBa [73] has extended PRISM to use also LDBAs.…”

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%

“…The source-code of both tools is located in the repository of Reference[47].Journal of the ACM, Vol. 67, No.…”

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confidence: 99%

A Unified Translation of Linear Temporal Logic to ω-Automata

Esparza

Křetínský

Sickert

2020

J. ACM

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“…We expect the LTL-to-DRW translation of this paper to produce automata similar in size (number of states, Rabin pairs) to the translations presented in [5,21], which have been implemented using Owl [7] and have been extensively tested. Indeed, the "Master Theorem" of [5,21] characterises the words satisfying a formula φ as those for which there exist sets M, N of subformulas satisfying three conditions, and so it has the same rough structure as our normal form.…”

Section: Preliminary Experimental Evaluationmentioning

confidence: 99%

An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata

Sickert

Esparza

2020

Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

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In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form n i =1 GFφ i ∨FGψ i , where φ i andψ i contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalisation procedures have a non-elementary worst-case blow-up, and follow an involved path from formulas to counter-free automata to star-free regular expressions and back to formulas. We improve on both points. We present a direct and purely syntactic normalisation procedure for LTL yielding a normal form, comparable to the one by Chang, Manna, and Pnueli, that has only a single exponential blow-up. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalises the formula, translates it into a special very weak alternating automaton, and applies a simple determinisation procedure, valid only for these special automata.CCS Concepts: • Theory of computation → Modal and temporal logics; Automata over infinite objects.where a ∈ Ap is an atomic proposition and X, U, W, R, and M are the next, (strong) until, weak until, (weak) release, and strong release operators, respectively.

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“…This is the current approach of ltlsynt [20]. However, since the introduction of the HOA format [2] allowing the representation of TELA, we have seen the development of several tools for converting LTL formulas into TELA: for instance delag [21], ltl2da and ltl2na (all three part of newer versions of Owl [13]), ltl3tela [19], or Spot's ltl2tgba -G (see Section 5), all trying to reduce the size of their output by using acceptance formulas more closely related to the input LTL formulas. An alternative way to transform an LTL formula into a DTPA is therefore to first transform the LTL formula into a deterministic TELA, and then "paritize" the result.…”

Section: Figures 1 and 3 On Page 9 Show An Example Of Input And Outputmentioning

confidence: 99%

Practical “Paritizing” of Emerson-Lei Automata

Renkin

Duret-Lutz

Pommellet

2020

Automated Technology for Verification and Analysis

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We introduce a new algorithm that takes a Transition-based Emerson-Lei Automaton (TELA), that is, an ω-automaton whose acceptance condition is an arbitrary Boolean formula on sets of transitions to be seen infinitely or finitely often, and converts it into a Transition-based Parity Automaton (TPA). To reduce the size of the output TPA, the algorithm combines and optimizes two procedures based on a latest appearance record principle, and introduces a partial degeneralization. Our motivation is to use this algorithm to improve our LTL synthesis tool, where producing deterministic parity automata is an intermediate step.

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Owl: A Library for $$\omega $$-Words, Automata, and LTL

Cited by 62 publications

References 34 publications

A Unified Translation of Linear Temporal Logic to ω-Automata

A Unified Translation of Linear Temporal Logic to ω-Automata

An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata

Practical “Paritizing” of Emerson-Lei Automata

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