Conversion Algorithm of Linear-Time Temporal Logic to Buchi Automata

Abstract

The size of Büchi Automata(BA) is a key factor during converting Linear-Time Temporal Logic(LTL) formulae to BA in model checking. Most algorithms for generating BA from LTL formulas involved intermediate automata, degeneralization algorithm and simplification of the formulas, but size of BA and time of converting can be reduced further. In this paper, we present an improved Tableau-based algorithm, which converts LTL formulae to Transition-based Büchi Automata(TBA) more efficiently. The algorithm is geared towards being used in model checking in on-the-fly fashion. By attaching the satisfy information of ∪-formula on states and transitions, we can decide whether the sequences of the BA are acceptable by using only one acceptance condition set, not multiple ones. Binary Decision Diagrams(BDD) is used to describe BA and simplify formulae. A better data structure, syntax Directed Acyclic Graph(DAG), is adopted in the algorithm. The size of product BA and computational complexity can be reduced significantly by using on-the-fly degeneralization. The algorithm can expand the state nodes while detecting the validity of nodes, removing the invalid nodes and combining equivalent states and transitions. Compared with other recent conversion tools, the algorithm proposed in this paper runs faster, with the smaller size of BA.

LTL Formulae to Buchi Automata Translation Using on‐the‐Fly De‐generalization

“…Our algorithm is an LTL-model checking algorithm by tableaux construction. It differs from the previous works [2,3,6] in two ways: 1) AD, which is a set of satisfied acceptance conditions, is attached to each state and transition in the automata.…”