# Limit Deterministic and Probabilistic Automata for LTL ∖ GU

@inproceedings{Kini2015LimitDA, title={Limit Deterministic and Probabilistic Automata for LTL ∖ GU}, author={Dileep Kini and Mahesh Viswanathan}, booktitle={TACAS}, year={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, with the restriction that no until operator occurs in the scope of an always operator. Our main result is the construction of Limit Deterministic Buchi automata for this logic that are exponential in the size of the formula. One consequence of our construction is a new, improved EXPTIME model checking…

## 20 Citations

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

- Computer ScienceATVA
- 2016

This work presents an extension of PRISM for LTL model checking of MDP using LDBA, a special subclass of limit-deterministic Buchi automata that can replace deterministic Rabin automata in quantitative probabilistic model checking algorithms.

### From LTL and Limit-Deterministic Büchi Automata to Deterministic Parity Automata

- Computer ScienceTACAS
- 2017

This paper describes a single exponential translation from limit-deterministic Buchi automata (LDBA) to DPA, and shows that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, “Safraless” LTL-to-DPA construction.

### 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.

### Controller Synthesis for MDPs and Frequency LTL\GU

- Computer Science, MathematicsLPAR
- 2015

Quantitative extensions of temporal logics have recently
attracted significant attention. In this work, we study
frequency LTL (fLTL), an extension of LTL which allows to speak
about frequencies of…

### Controller synthesis for MDPs and Frequency LTL \

- Computer Science, Mathematics
- 2015

Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of…

### Controller synthesis for MDPs and Frequency LTL$\setminus$GU

- Computer Science, MathematicsArXiv
- 2015

This work shows that the problem is decidable for the fragment fLTL$\setminus$GU, where U does not occur in the scope of G (but still F can) and based on a novel translation of such quantitative formulae into equivalent deterministic automata.

### 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.

### 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.

### 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.

### L O ] 1 4 Se p 20 15 Controller synthesis for MDPs and Frequency LTL \

- Computer Science, Mathematics
- 2020

Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of…

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