From LTL to unambiguous Büchi automata via disambiguation of alternating automata

Research output: Contribution to journalResearch articleContributedpeer-review


Due to the high complexity of translating linear temporal logic (LTL) to deterministic automata, several forms of “restricted” nondeterminism have been considered with the aim of maintaining some of the benefits of deterministic automata, while at the same time allowing more efficient translations from LTL. One of them is the notion of unambiguity. This paper proposes a new algorithm for the generation of unambiguous Büchi automata (UBA) from LTL formulas. Unlike other approaches it is based on a known translation from very weak alternating automata (VWAA) to NBA. A notion of unambiguity for alternating automata is introduced and it is shown that the VWAA-to-NBA translation preserves unambiguity. Checking unambiguity of VWAA is determined to be PSPACE-complete, both for the explicit and symbolic encodings of alternating automata. The core of the LTL-to-UBA translation is an iterative disambiguation procedure for VWAA. Several heuristics are introduced for different stages of the procedure. We report on an implementation of our approach in the tool Duggi and compare it to an existing LTL-to-UBA implementation in the SPOT tool set. Our experiments cover model checking of Markov chains, which is an important application of UBA.


Original languageEnglish
Pages (from-to)42–82
Number of pages41
JournalFormal Methods in System Design
Publication statusPublished - 15 Dec 2021

External IDs

Scopus 85121381299
ORCID /0000-0002-5321-9343/work/142236685


DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis

ASJC Scopus subject areas


  • omega-automata, Unambiguous Büchi Automata, linear temporal logic, verification, alternating automata