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Determinization and Limit-determinization of Emerson-Lei automata [article]

Tobias John, Simon Jantsch, Christel Baier, Sascha Klüppelholz
2021 arXiv   pre-print
We study the problem of determinizing ω-automata whose acceptance condition is defined on the transitions using Boolean formulas, also known as transition-based Emerson-Lei automata (TELA).  ...  We also study limit-determinization of TELA and show that this can be done with a single-exponential blow-up, in contrast to the known double-exponential lower-bound for determinization.  ...  We thank David Müller for suggesting to us the problem of determinizing Emerson Lei automata and many discussions on the topic.  ... 
arXiv:2106.15892v1 fatcat:rgx7n2ba6rbmvalnmyiktf5rxu

LTL to Deterministic Emerson-Lei Automata

David Müller, Salomon Sickert
2017 Electronic Proceedings in Theoretical Computer Science  
We introduce a new translation from linear temporal logic (LTL) to deterministic Emerson-Lei automata, which are omega-automata with a Muller acceptance condition symbolically expressed as a Boolean formula  ...  We identify two fragments of LTL, for which one can easily construct deterministic automata and show how knowledge of these components can reduce the number of states.  ...  , which we call Emerson-Lei acceptance.  ... 
doi:10.4204/eptcs.256.13 fatcat:yuqy6plainhctau6qr2kkgt3iy

A new heuristic for bad cycle detection using BDDs [chapter]

R. H. Hardin, R. P. Kurshan, S. K. Shukla, M. Y. Vardi
1997 Lecture Notes in Computer Science  
It is a variation on a standard implementation of the Emerson-Lei algorithm, which our experimental data suggests can result in a significant speed-up for verification runs that pass.  ...  We conclude that this heuristic can be used to advantage on "mature" designs for which the anticipated result of the verification is pass.  ...  Bad Cycle Detection Based on The Emerson-Lei Formula In [EL86] Emerson and Lei introduced a/z-calculus formula of alternation depth 1, which expressed an FCTL fairness constraint.  ... 
doi:10.1007/3-540-63166-6_27 fatcat:vw7haru5kjbipfzj5apazptwy4

An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps [chapter]

Roderick Bloem, Harold N. Gabow, Fabio Somenzi
2000 Lecture Notes in Computer Science  
The algorithm can be used to decide emptiness of Büchi automata with the same complexity bound, improving Emerson and Lei's quadratic bound, and emptiness of Streett automata, with a similar bound in terms  ...  The algorithm performs Θ(n log n) image and preimage computations in the worst case, where n is the number of nodes in the graph. This is an improvement over the previously known quadratic bound.  ...  Emerson and Lei [EL87] and Kurshan [Kur94] propose explicit algorithms for deciding emptiness of Streett automata.  ... 
doi:10.1007/3-540-40922-x_4 fatcat:dvqeyrd7obhstamghl4e5deo5q

An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps

Roderick Bloem, Harold N. Gabow, Fabio Somenzi
2006 Formal methods in system design  
Emerson and Lei [9] and Kurshan [19] propose explicit algorithms for deciding emptiness of Streett automata. We combine their approach with our SCC-decomposition  ...  We shall discuss problems on which Lockstep performs worse that the algorithm of Emerson and Lei.  ...  Complexity of the Emerson-Lei algorithm Because of the practical importance of the Emerson-Lei algorithm for Büchi emptiness, we shall analyze its complexity in more detail.  ... 
doi:10.1007/s10703-006-4341-z fatcat:dsgm453mcrcxbnword4wxhqk2i

Model Checking: Historical Perspective and Example (Extended Abstract) [chapter]

Edmund M. Clarke, Sergey Berezin
1998 Lecture Notes in Computer Science  
An exhaustive search of the global state transition graph or system model is used to determine if the specification is true or not.  ...  In this paper we describe the theory underlying this technique and outline its historical development.  ...  Emerson and Lei [16] extended their result to show that formulas of the logic CTL*, which combines both branching-time and linear-time operators, could be checked with essentially the same complexity  ... 
doi:10.1007/3-540-69778-0_3 fatcat:flyys7zuefhpzou562dwv7hufa

Divide and Compose: SCC Refinement for Language Emptiness [chapter]

Chao Wang, Roderick Bloem, Gary D. Hachtel, Kavita Ravi, Fabio Somenzi
2001 Lecture Notes in Computer Science  
We show that our algorithm significantly outperforms the one of Emerson and Lei.  ...  We propose a refinement approach to symbolic SCC analysis, which performs large parts of the computation on abstracted systems, and on small subsets of the state space.  ...  We first compare the D'n'C algorithm to the one by Emerson and Lei.  ... 
doi:10.1007/3-540-44685-0_31 fatcat:46borrqyw5ebrdpwohyh3ev6ui

Relating Hierarchy of Temporal Properties to Model Checking [chapter]

Ivana Černá, Radek Pelánek
2003 Lecture Notes in Computer Science  
Emerson-Lei algorithm) with a quadratic number of symbolic steps (for an overview of symbolic algorithms see [11] ).  ...  The transition function determines four types of automata: deterministic, nondeterministic, universal, and alternating.  ... 
doi:10.1007/978-3-540-45138-9_26 fatcat:zllmtn2c7rekzgtde7xj5z4l2m

The Reactive Synthesis Competition (SYNTCOMP): 2018-2021 [article]

Swen Jacobs, Guillermo A. Perez, Remco Abraham, Veronique Bruyere, Michael Cadilhac, Maximilien Colange, Charly Delfosse, Tom van Dijk, Alexandre Duret-Lutz, Peter Faymonville, Bernd Finkbeiner, Ayrat Khalimov (+13 others)
2022 arXiv   pre-print
Finally, we present and analyze the results of our experimental evaluations, including a ranking of tools with respect to quantity and quality of solutions.  ...  Then, we introduce new benchmark classes that have been added to the SYNTCOMP library and give an overview of the participants of SYNTCOMP.  ...  For SYNTCOMP 2021 the following major changes have been applied (Meyer and Sickert, 2021 ): • LTL formulas are now translated to transitionbased deterministic Emerson-Lei automata (tDELA) by combining  ... 
arXiv:2206.00251v1 fatcat:qvg2cqgvjvaa7kpfd3nrbj4ahu

Model checking with generalized Rabin and Fin-less automata

Vincent Bloemen, Alexandre Duret-Lutz, Jaco van de Pol
2019 International Journal on Software Tools for Technology Transfer (STTT)  
In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness.  ...  We show how to convert TGRAs into automata with Fin-less acceptance and show how a TGBA emptiness procedure can be extended to check Fin-less automata.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10009-019-00508-4 fatcat:gs6jxx3j7fdzzoqpz5kfgfcllu

Evaluating LTL Satisfiability Solvers [chapter]

Viktor Schuppan, Luthfi Darmawan
2011 Lecture Notes in Computer Science  
It takes the benchmark families of previous studies, which only have a limited overlap, and adds benchmark families not used for that purpose before.  ...  The same authors compare symbolic constructions of Büchi automata in [59] using the BDD-based engine of Cadence SMV as backend solver.  ...  This triggered us to implement a forward version (e.g., [40] ) of the Emerson-Lei algorithm in NuSMV-BDD. rozier formulas.  ... 
doi:10.1007/978-3-642-24372-1_28 fatcat:73zzxfweh5ep7nyqvxzsoeax7u

Efficient ω-regular language containment [chapter]

Ramin Hojati, Herve Touati, Robert P. Kurshan, Robert K. Brayton
1993 Lecture Notes in Computer Science  
The main computation involves building the product machine of the system and specification, and then checking for cycles not contained in any of the cycle sets (these are sets of states specified by the  ...  One method for proving properties about a design is by using L-automata [Kur90].  ...  The Emerson-Lei Method and Modifications In this section, we introduce four algorithms for the language containment cheek.  ... 
doi:10.1007/3-540-56496-9_31 fatcat:cxc5tkcmofejvpr75us6x2pt7i

Page 3212 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
In particular we are interested in the sublanguages of PuS determined by the value of the Emerson- Lei alternation depth.  ...  With limits of state durations, one can treat conventional liveness and fairness, and can also measure liveness and fairness through properties of limits.  ... 

Sharp Disjunctive Decomposition for Language Emptiness Checking [chapter]

Chao Wang, Gary D. Hachtel
2002 Lecture Notes in Computer Science  
The decomposition is "sharp" in the sense that it allows BDD operations on the concrete model to be restricted to small subspaces, and that unfair and unreachable parts of the submodules and automaton  ...  union of which is exactly the language accepted by the original system.  ...  Acknowledgements We acknowledge the contributions of "deep in the shed" research sessions with Roderick Bloem, Kavita Ravi, and Fabio Somenzi.  ... 
doi:10.1007/3-540-36126-x_7 fatcat:hn5kxsoqwvcy7dxqckr2w7dzru

Efficient Büchi Universality Checking [chapter]

Seth Fogarty, Moshe Y. Vardi
2010 Lecture Notes in Computer Science  
The complementation of Büchi automata, required for checking automata universality, remains one of the outstanding automata-theoretic challenges in formal verification.  ...  We extend the subsumption technique of Ben-Amram and Lee to the general case of Büchi universality problems, and experimentally demonstrate the necessity of subsumption for the scalability of the Ramsey-based  ...  A classical approach is Emerson-Lei backward-traversal nested fixpoint νY.μX.(X ∪ (Y ∩ F )) [8] .  ... 
doi:10.1007/978-3-642-12002-2_17 fatcat:7ntaqt3byfgo3exa65u5l2zy6i
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