# MoChiBA: Probabilistic LTL Model Checking Using Limit-Deterministic Büchi Automata

@inproceedings{Sickert2016MoChiBAPL, title={MoChiBA: Probabilistic LTL Model Checking Using Limit-Deterministic B{\"u}chi Automata}, author={Salomon Sickert and Jan Křet{\'i}nsk{\'y}}, booktitle={ATVA}, year={2016} }

The limiting factor for quantitative analysis of Markov decision processes (MDP) against specifications given in linear temporal logic (LTL) is the size of the generated product. As recently shown, a special subclass of limit-deterministic Buchi automata (LDBA) can replace deterministic Rabin automata in quantitative probabilistic model checking algorithms. We present an extension of PRISM for LTL model checking of MDP using LDBA. While existing algorithms can be used only with minimal changes…

## 28 Citations

### Rabinizer 4: From LTL to Your Favourite Deterministic Automaton

- Computer ScienceCAV
- 2018

Rabinizer 4 is presented, a tool set for translating formulae of linear temporal logic to different types of deterministic \(\omega \)-automata and enhancements both in terms of the size of the automata and the computational time are shown, due to algorithmic as well as implementation improvements.

### LTL to Deterministic Emerson-Lei Automata

- Computer ScienceGandALF
- 2017

A new translation from linear temporal logic to deterministic Emerson-Lei automata with a Muller acceptance condition symbolically expressed as a Boolean formula is introduced, which is an enhanced product construction that exploits knowledge of its components to reduce the number of states.

### Seminator 2 Can Complement Generalized Büchi Automata via Improved Semi-determinization

- Computer ScienceCAV
- 2020

The second generation of the tool Seminator that transforms transition-based generalized Büchi automata (TGBAs) into equivalent semi-deterministic automata is presented, providing a new way to complement automata that is competitive with state-of-the-art complementation tools.

### Good-for-MDPs Automata

- Computer ScienceArXiv
- 2019

The promise of GFM automata is demonstrated by defining a new class of automata with favorable properties - they are Buchi Automata with low branching degree obtained through a simple construction - and it is shown that going beyond limit-deterministic automata may significantly benefit reinforcement learning.

### A Unified Translation of Linear Temporal Logic to ω-Automata

- Computer Science
- 2020

A unified translation of LTL formulas into nondeterministic Buchi automata, limit-deterministic LTL automata (LDBA), and deterministic Rabin Automata (DRA) is presented.

### Seminator: A Tool for Semi-Determinization of Omega-Automata

- Computer ScienceLPAR
- 2017

The tool Seminator accepts transition-based generalized Buchi automata (TGBA) as an input and produces automata with two kinds of semi-determinism, and the implemented procedure performs degeneralization and semi-Determinization simultaneously and employs several other optimizations.

### LTLf Synthesis on Probabilistic Systems

- Computer ScienceGandALF
- 2020

Two algorithms for solving policy synthesis for MDP behaviors given finite-trace properties of Linear Temporal Logic over finite traces are presented: the first via reduction of LTLf to LTL and the second using native tools for LTL f.

### Reinforcement Learning for Temporal Logic Control Synthesis with Probabilistic Satisfaction Guarantees

- Computer Science2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

A model-free reinforcement learning algorithm to synthesize control policies that maximize the probability of satisfying high-level control objectives given as Linear Temporal Logic formulas, which is even more general than a fully unknown MDP.

### LTL-Constrained Steady-State Policy Synthesis

- Computer Science
- 2021

A unified solution reducing the multi-type specification to a multi-dimensional long-run average reward for Markov decision processes (MDP) is provided, enabled by Limit-Deterministic Büchi Automata (LDBA) and allows for an elegant solution through a simple linear programme.

### LTL-Constrained Steady-State Policy Synthesis

- Computer ScienceIJCAI
- 2021

A unified solution reducing the multi-type specification to a multi-dimensional long-run average reward for Markov decision processes (MDP) is provided, enabled by Limit-Deterministic Büchi Automata (LDBA) and allows for an elegant solution through a simple linear programme.

## References

SHOWING 1-10 OF 36 REFERENCES

### Limit Deterministic and Probabilistic Automata for LTL ∖ GU

- Computer Science, MathematicsTACAS
- 2015

LTL i¾? GU is a fragment of linear temporal logic LTL, where negations appear only on propositions, and formulas are built using the temporal operators X next, F eventually, G always, and U until,…

### Rabinizer 3: Safraless Translation of LTL to Small Deterministic Automata

- Computer ScienceATVA
- 2014

This paper presents a tool for translating LTL formulae into deterministic ω-automata, the first tool that covers the whole LTL that does not use Safra’s determinization or any of its variants, and shows that this leads to significant speed-up of probabilistic LTL model checking, especially with the generalized Rabin automata.

### Rabinizer 2: Small Deterministic Automata for LTL ∖ GU

- Computer ScienceATVA
- 2013

A tool that generates automata for LTL(X,F,G,U) where U does not occur in any G-formula (but F still can) where DGRA have been recently shown to be as useful in probabilistic model checking as DRA.

### Automata with Generalized Rabin Pairs for Probabilistic Model Checking and LTL Synthesis

- Computer ScienceCAV
- 2013

This work considers deterministic automata with acceptance condition given as disjunction of generalized Rabin pairs (DGRW) as an alternative to DRW, and presents algorithms for probabilistic model-checking as well as game solving for DGRW conditions.

### Lazy Probabilistic Model Checking without Determinisation

- Computer ScienceCONCUR
- 2015

It is shown that full determinisation can be avoided: subset and breakpoint constructions suffice, and the approach is implemented---both explicit and symbolic versions---in a prototype tool.

### Limit-Deterministic Büchi Automata for Linear Temporal Logic

- Computer ScienceCAV
- 2016

This work presents a direct construction from an LTL formula \(\varphi \) to a limit-deterministic Buchi automaton, which yields much smaller automata for formulas with deep nesting of modal operators and performs at least as well as the existing approaches on general formulas.

### Efficient Büchi Automata from LTL Formulae

- Computer ScienceCAV
- 2000

We present an algorithm to generate small Buchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure,…

### Deterministic Automata for the (F,G)-fragment of LTL

- Computer ScienceCAV
- 2012

This work presents a direct translation of the ( F, G )-fragment of LTL into deterministic ω-automata with no determinization procedure involved and investigates the complexity of this translation and provides experimental results and compare them to the traditional method.

### An Optimal Automata Approach to LTL Model Checking of Probabilistic Systems

- Computer ScienceLPAR
- 2003

This study shows that checking whether a probabilistic system satisfies an ω-automaton with positive probability can be solved in linear time for this kind of automata, and extends the study to the evaluation of this probability.

### 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…