One Theorem to Rule Them All

Esparza, Javier; Křetínský, Jan; Sickert, Salomon

doi:10.1145/3209108.3209161

Cited by 23 publications

(20 citation statements)

References 36 publications

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“…The starting point of this paper is the observation that some results of [5,21] allow us to easily derive a normal form for LTL, albeit only when LTL is interpreted on stable words. More precisely, in Section 5 we show that for every…”

Section: Stable Wordsmentioning

confidence: 99%

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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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Section: Stable Wordsmentioning

confidence: 99%

“…It is presented in Sections 4 to 6, modulo the omission of some straightforward induction cases. To make this paper self-contained, the proofs of three lemmas taken from [5,21] are reproduced in Appendix A. We have mechanised the complete correctness proof in Isabelle/HOL [15], building upon previous work [1,19,20].…”

Section: Introductionmentioning

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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“…For all these fragments several translations to deterministic automata are known and we are going to use the constructions for µLT L, νLT L, GF(µLT L), and FG(νLT L) described in [13], for G(µLT L) and F(νLT L) the construction described in [38], and for arbitrary LTL formulas the construction described in [12]. It should be noted that of course these constructions can be swapped with other constructions, but some of the implemented heuristics rely on the specific state structure these constructions yield.…”

Section: -G(µlt L) and F(νlt L)mentioning

confidence: 99%

“…-If we encounter W(ϕ), then ϕ ∈ µLT L ∪ νLT L. By using the construction of [13] the state q ′ is in fact a Boolean formula over modal operators treated as variables. Let V be the set of variables and let M be the set of satisfying assignments of q ′ .…”

Section: Quality Scoresmentioning

confidence: 99%

“…We, on the other hand, address the 'messy state space' issue by employing a collection of 'Safraless' LTL to deterministic parity automaton (DPA) translations [38,12,13] in combination with a special product automaton construction that includes a latest appearance record (LAR) construction and a formula decomposition in the spirit of [34,15,10,35]. Our construction recovers the Boolean structure present in the input specification.…”

Section: Introductionmentioning

confidence: 99%

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Practical synthesis of reactive systems from LTL specifications via parity games

2019

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You can teach an old dog new tricks: making a classic approach structured, forward-explorative, and incremental. Abstract The synthesis of reactive systems from linear temporal logic (LTL) specifications is an important aspect in the design of reliable software and hardware. We present our adaption of the classic automata-theoretic approach to LTL synthesis, implemented in the tool Strix which has won the two last synthesis competitions (Syntcomp2018/2019). The presented approach is (1) structured, meaning that the states used in the construction have a semantic structure that is exploited in several ways, it performs a (2) forward exploration such that it often constructs only a small subset of the reachable states, and it is (3) incremental in the sense that it reuses results from previous inconclusive solution attempts. Further, we present and study different guiding heuristics that determine where to expand the on-demand constructed arena. Moreover, we show several techniques for extracting an implementation (Mealy machine or circuit) from the witness of the tree-automaton emptiness check. Lastly, the chosen constructions use a symbolic representation of the transition functions to reduce runtime and memory consumption. We evaluate the proposed techniques on the Syntcomp2019 benchmark set and show in more detail how the proposed techniques compare to the techniques implemented in other leading LTL synthesis tools.

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