An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata

In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form $\bigwedge_{i=1}^n \mathbf{G}\mathbf{F} \varphi_i \vee \mathbf{F}\mathbf{G} \psi_i$, where $\varphi_i$ and $\psi_i$ contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalisation procedures have a non-elementary worst-case blow-up, and follow an involved path from formulas to counter-free automata to star-free regular expressions and back to formulas. We improve on both points. We present a direct and purely syntactic normalisation procedure for LTL yielding a normal form, comparable to the one by Chang, Manna, and Pnueli, that has only a single exponential blow-up. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalises the formula, translates it into a special very weak alternating automaton, and applies a simple determinisation procedure, valid only for these special automata.Comment: This is the extended version of the referenced conference paper and contains an appendix with additional materia

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Abstract. Several optimal algorithms have been proposed for the complementation of nondeterministic Büchi word automata. Due to the intricacy of the problem and the exponential blow-up that complementation involves, these algorithms have never been used in practice, even though an effective complementation construction would be of significant practical value. Recently, Kupferman and Vardi described a complementation algorithm that goes through weak alternating automata and that seems simpler than previous algorithms. We combine their algorithm with known and new minimization techniques. Our approach is based on optimizations of both the intermediate weak alternating automaton and the final nondeterministic automaton, and involves techniques of rank and height reductions, as well as direct and fair simulation.

My gratitude extends to Hongjoon Shin, Byungho Kim, Jaeyong Chung,

At first, I would like to express sincere gratitude to my advisor, Dr. Jacob A. Abraham for his support and insightful advice. He always encourages me to look at the big picture, and at the same time look at the fundamentals of the problem. His encouragement helped me greatly in doing the right research successfully. With his enthusiasm and breadth of knowledge, I could enjoy the long journey of Ph.D. research. I also would like to thank to Dr. Nur Touba