# A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

@inproceedings{Brunner2019AVA, title={A Verified and Compositional Translation of LTL to Deterministic Rabin Automata}, author={Julian Brunner and Benedikt Seidl and Salomon Sickert}, booktitle={ITP}, year={2019} }

We present a formalisation of the unified translation approach from linear temporal logic (LTL) to ω-automata from [19]. This approach decomposes LTL formulas into “simple” languages and allows a clear separation of concerns: first, we formalise the purely logical result yielding this decomposition; second, we develop a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the “simple” languages; third, we instantiate this generic theory…

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## References

SHOWING 1-10 OF 20 REFERENCES

### Verifying the LTL to Büchi Automata Translation via Very Weak Alternating Automata

- Computer ScienceITP
- 2018

This work presents a formalization of a translation from LTL formulae to generalized Buchi automata in the HOL4 theorem prover, and uses the CakeML compiler to generate fully verified machine code implementing the translation.

### One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata

- Computer ScienceLICS
- 2018

A unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic Büchi Automata, and nondeterministicBüchi automata derived from one single Master Theorem of purely logical nature is presented.

### From LTL to Deterministic Automata: A Safraless Compositional Approach

- Computer ScienceCAV
- 2014

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula i¾?. The automaton is the product of a master automaton and an array of slave automata, one…

### Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

- Computer ScienceTPHOLs
- 2009

The correctness and termination of the implementation of a translation of LTL formulae into Buchi automata are proven in Isabelle/HOL, and executable code is generated using the Isabelle /HOL code generator.

### Simple on-the-fly automatic verification of linear temporal logic

- Computer SciencePSTV
- 1995

A tableau-based algorithm for obtaining an automaton from a temporal logic formula that can be constructed simultaneously with, and guided by, the generation of the model, and which can be used in model checking in an “on-the-fly” fashion.

### The CAVA Automata Library

- Computer ScienceArch. Formal Proofs
- 2014

The formalization techniques presented here allow an extension of the graph and automata library in the CAVA model checker to a wider scope, and are not limited to graph libraries, but apply to class hierarchies in general.

### A Fully Verified Executable LTL Model Checker

- Computer Science, MathematicsCAV
- 2013

An LTL model checker whose code has been completely verified using the Isabelle theorem prover is presented, which leads to a checker that can already be used as a trusted reference implementation against which advanced implementations can be tested.

### Transition Systems and Automata

- Computer ScienceArch. Formal Proofs
- 2017

This entry provides a very abstract theory of transition systems that can be instantiated to express various types of automata, and comes with instantiations for DFAs, NFAs, and Büchi automata.

### Principles of model checking

- Computer Science
- 2008

Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.

### Automatic verification of probabilistic concurrent finite state programs

- Computer Science26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
- 1985

An automata-theoretic approach is described, whereby probabilistic quantification over sets of computations is reduced to standard quantificationover individual computations, and a new determinization construction for ω-automata is used to improve the time complexity of the algorithm by two exponentials.